GlossaryT.Slope History

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February 04, 2009, at 03:44 AM by LFS -
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[]LFS - contact - website

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[]LFS - contact - website

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[]Freeware - Available for Offline and Online Use - Translatable (html)

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[]Freeware - Available for School and Offline and Online Use - Translatable (html)

October 03, 2008, at 06:52 AM by LFS -
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September 28, 2008, at 09:39 AM by LFS -
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[tableend]
ans-odg

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[tableend]

September 08, 2008, at 01:59 PM by LFS -
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Slope & Speed - InterActivity
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Slope & Speed - InterActivity  NEW!
September 08, 2008, at 01:59 PM by LFS -
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Slope & Speed - InterActivity
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Slope & Speed - InterActivity
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Slope & Speed - InterActivity
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Slope & Speed - InterActivity
September 05, 2008, at 02:29 PM by LFS -
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Introduction to Slopes 1.1 - Mathcast: Money in the Bank

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Introduction to Slopes 1.1 - Mathcast: Money in the Bank

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Introduction to Slopes 1.2 - Mathcast: More Positive
Introduction to Slopes 1.3 - Mathcast: Slope & Speed

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Introduction to Slopes 1.2 - Mathcast: More Positive
Introduction to Slopes 1.3 - Mathcast: Slope & Speed

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Introduction to Slopes 1.4 - Mathcast: Formula for Slope
Introduction to Slopes 1.5 - Mathcast: Calculating Slope

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Introduction to Slopes 1.4 - Mathcast: Formula for Slope
Introduction to Slopes 1.5 - Mathcast: Calculating Slope

September 05, 2008, at 02:22 PM by LFS -
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Introduction to Slopes 1.5 - Mathcast: Calculating Slope

August 21, 2008, at 09:16 PM by LFS -
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Introduction to Slopes 1.4 - Mathcast: Formula for Slope

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Introduction to Slopes 1.4 - Mathcast: Formula for Slope

August 21, 2008, at 03:14 PM by LFS -
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Introduction to Slopes 1.4 - Mathcast: Formula for Slope

August 21, 2008, at 08:11 AM by LFS -
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Introduction to Slopes 1.3 - Mathcast: Slope & Speed

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Introduction to Slopes 1.3 - Mathcast: Slope & Speed

August 21, 2008, at 08:11 AM by LFS -
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Mathcasts         Examples      Practice    More      S

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Mathcasts         Examples      Practice    More      S

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Introduction to Slopes 1.1 - Mathcast: Money in the Bank

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Introduction to Slopes 1.1 - Mathcast: Money in the Bank

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Introduction to Slopes 1.2 - Mathcast: More Positive
Introduction to Slopes 1.3 - Mathcast: Slope & Speed

Slope & Speed - InterActivity
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Introduction to Slopes 1.2 - Mathcast: More Positive
Introduction to Slopes 1.3 - Mathcast: Slope & Speed

Slope & Speed - InterActivity
August 21, 2008, at 08:10 AM by LFS -
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Introduction to Slopes 1.1 - Mathcast: Money in the Bank

Money in the Bank: Worksheet

Introduction to Slopes 1.2 - Mathcast: More Positive
Introduction to Slopes 1.3 - Mathcast: Slope & Speed

Slope & Speed - InterActivity
to:

Introduction to Slopes 1.1 - Mathcast: Money in the Bank

Money in the Bank: Worksheet

Introduction to Slopes 1.2 - Mathcast: More Positive
Introduction to Slopes 1.3 - Mathcast: Slope & Speed

Slope & Speed - InterActivity
August 21, 2008, at 08:09 AM by LFS -
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Introduction to Slopes 1.1 - Mathcast

Money in the Bank - Worksheet

Introduction to Slopes 1.2 - Mathcast
Introduction to Slopes 1.3 - Mathcast

Money in the Bank - InterActivity
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Introduction to Slopes 1.1 - Mathcast: Money in the Bank

Money in the Bank: Worksheet

Introduction to Slopes 1.2 - Mathcast: More Positive
Introduction to Slopes 1.3 - Mathcast: Slope & Speed

Slope & Speed - InterActivity
August 21, 2008, at 08:07 AM by LFS -
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Money in the Bank - Applet
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Money in the Bank - InterActivity
August 21, 2008, at 08:06 AM by LFS -
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Money in the Bank - Worksheet
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Money in the Bank - Worksheet

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Money in the Bank - Applet
August 20, 2008, at 11:23 AM by LFS -
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Mathcasts         Examples      Practice    More      S

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Mathcasts         Examples      Practice    More      S

August 20, 2008, at 11:22 AM by LFS -
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August 20, 2008, at 11:20 AM by LFS -
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August 20, 2008, at 11:18 AM by LFS -
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5 InterActivities to Practice Slope!

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InterActivities: 5 InterActivities to Practice Slope

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[c  width=306]

August 20, 2008, at 11:11 AM by LFS -
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5 InterActivities to Practice Slope!

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5 InterActivities to Practice Slope!

August 20, 2008, at 11:04 AM by LFS -
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  • Think: slope=speed. Speed is measured distance/time (mph or m/s). Time = x-axis and distance = y-axis.
to:
  • Think: slope=speed. Speed is measured distance/time (mph or m/s) where time = x-axis and distance = y-axis.
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[row]
[]
5 InterActivities to Practice Slope!

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[  width=110px] Global
[]Slope of a line

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[]Brief
[]Mathcasts and Interactivities to understand and practice the slope of a line in the Cartesaian plane.

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[]Grade
[]7-10    Interactivities start at 7th grade level on up

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[]Strand
[]Algebra and Functions / Geometry and Measurement
[row]
[]Standard
[]CA 7AF.3.3
[row]
[]Keywords
[]line, slope, linear equation, change in y, change in x, ratio
[row]
[]Comments
[]none
[row]
[]Download
[] 
[row]
[]Author
[]LFS - contact - website
[row]
[]Type
[]Freeware - Available for Offline and Online Use - Translatable (html)
[row]
[]Use
[]Requires sunJava player

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August 20, 2008, at 10:54 AM by LFS -
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Introduction to Slopes 1.3 - Mathcast

August 20, 2008, at 08:24 AM by LFS -
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Definition: The slope of a line is the rate of change, that is the: "vertical change"/"horizontal change".

to:

Definition: The slope is the rate of change of a line, that is the: "vertical change"/"horizontal change".

August 20, 2008, at 08:20 AM by LFS -
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Mathcasts         Examples      Practice    More      S

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Mathcasts         Examples      Practice    More      S

August 20, 2008, at 08:07 AM by LFS -
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August 20, 2008, at 08:05 AM by LFS -
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Introduction to Slopes 1.1 - Mathcast
Introduction to Slopes 1.2 - Mathcast
Money in the Bank - Worksheet

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Introduction to Slopes 1.1 - Mathcast
Introduction to Slopes 1.2 - Mathcast
Money in the Bank - Worksheet

August 20, 2008, at 05:04 AM by LFS -
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[tableend]

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Let's "pick" the points root=(3,0) and y-intercept=(0,-6).

to:

Let's "pick" the points root=(3,0) and y-intercept=(0,-6).

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  • Coordinates of a point are (x,y) so when graphing a point do horizontal then vertical. See&Do
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  • Coordinates of a point are (x,y) so when graphing a point do horizontal then vertical. See&Do

[row]
[ colspan=2]

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[tableend]

August 20, 2008, at 04:59 AM by LFS -
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[table border=1 cellpadding=3]

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[c width=310]


[] To calculate the slope we "pick" points on the line A(1,-4) and B(4,2).

We will look "from A to B".
to:
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Added lines 25-31:

[c width=310]


[] To calculate the slope we "pick" points on the line A(1,-4) and B(4,2).

We will look "from A to B".

[table border=1 cellpadding=3]
[row]

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Introduction to Slopes - Money in the Bank

August 19, 2008, at 03:28 AM by LFS -
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  1. slope =   \frac{\mbox{change in y}}{\mbox{change in x}}
to:
  1. slope =   \frac{\mbox{change in y}}{\mbox{change in x}}
August 19, 2008, at 02:49 AM by LFS -
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[table border=1 bordercolor=#ee8800 cellspacing=3]
[row]
[]

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[row]
[]

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[tableend]

August 19, 2008, at 02:47 AM by LFS -
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[](0,-6)Slope = m =  \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{-6}{-3} = 2 .

to:

[]Slope = m =  \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{-6}{-3} = 2 .

August 19, 2008, at 02:46 AM by LFS -
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[]"change in x" = 0-3 = -3

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[]"change in x" = 0-3 = -3 and "change in y" = -6-0 = -6
[tableend]

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"change in y" = -6-0 = -6
[tableend]

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BUT you must do the subtractions in the same direction! See Calculating Slope.

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BUT you must do the subtractions in the same direction!

August 19, 2008, at 02:43 AM by LFS -
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[] To calculate the slope we "pick" points on the line A(1,-4) and B(4,2).

to:


[] To calculate the slope we "pick" points on the line A(1,-4) and B(4,2).

Changed line 41 from:

to:

Changed lines 43-44 from:

Let's "pick" the points root=(3,0) and y-intercept=(0,-6).

So (3,0) is our first point and (0,-6) is our second point.
to:

Let's "pick" the points root=(3,0) and y-intercept=(0,-6).

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[]Slope = m =  \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{-6}{-3} = 2 .

to:

[](0,-6)Slope = m =  \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{-6}{-3} = 2 .

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ans-odg

August 19, 2008, at 02:37 AM by LFS -
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[] To calculate the slope we "pick" points on the line A(1,-4) and B(4,2).

to:

[] To calculate the slope we "pick" points on the line A(1,-4) and B(4,2).

Changed lines 43-51 from:
to:

Let's "pick" the points root=(3,0) and y-intercept=(0,-6).

So (3,0) is our first point and (0,-6) is our second point.
     Remember - we subtract "second point" - "first point".
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[ colspan=2]

  • Coordinates of a point are (x,y) so when graphing a point do horizontal then vertical. See&Do

[row]
[ colspan=2]

  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so with slope the vertical change is above the horizontal change in the fraction!
to:

[]"change in x" = 0-3 = -3

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"change in y" = -6-0 = -6
[tableend]

[table border=1 cellpadding=3]

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[]Slope = m =  \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{-6}{-3} = 2 .
[tableend]

[table border=2 bordercolor=#990000 cellpadding=3]
[row]
[]Slope is same no matter what points we "pick".
[tableend]

 

BUT you must do the subtractions in the same direction! See Calculating Slope.

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Introduction to Slopes - Money in the Bank

Calculating the slope of a line:

  1. Pick any 2 points on the line.
  2. Arbitrarily decide which is the "first point" and "second point".
  3. "change in x" = "x-coordinate of second point" - "x-coordinate of first point".
  4. "change in y" = "y-coordinate of second point" - "y-coordinate of first point".
  5. slope =   \frac{\mbox{change in y}}{\mbox{change in x}}

Rule: The slope of a line is a number. Parallel lines have the same slope.

to:
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[]
1. Click on the New point tool. In the drawing pad, find the point with coordinates (1,1) and then click. Point A should be drawn. Check the coordinates of point A by rolling your mouse over it.

to:
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to:

Introduction to Slopes - Money in the Bank

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3. Find the coordinates and draw the points C(5,4) and D(5,1).

to:

Calculating the slope of a line:

  1. Pick any 2 points on the line.
  2. Arbitrarily decide which is the "first point" and "second point".
  3. "change in x" = "x-coordinate of second point" - "x-coordinate of first point".
  4. "change in y" = "y-coordinate of second point" - "y-coordinate of first point".
  5. slope =   \frac{\mbox{change in y}}{\mbox{change in x}}
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4. Use the Segment tool and make the rectangle ABCD.

to:

Rule: The slope of a line is a number. Parallel lines have the same slope.


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1. Click on the New point tool. In the drawing pad, find the point with coordinates (1,1) and then click. Point A should be drawn. Check the coordinates of point A by rolling your mouse over it.

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to:
Added lines 125-137:
August 19, 2008, at 02:26 AM by LFS -
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[]Slope of this line = m =  \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{6}{3} = 2

to:

[]Slope of this line = m =  \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{6}{3} = 2

August 19, 2008, at 02:25 AM by LFS -
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Calculating the slope of a line:

to:

Calculating the slope of a line:

August 19, 2008, at 02:24 AM by LFS -
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Rule: The slope of a line is a number. Parallel lines have the same slope.

to:

Introduction to Slopes - Money in the Bank

Calculating the slope of a line:

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Rule: The slope of a line is a number. Parallel lines have the same slope.

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Introduction to Slopes - Money in the Bank

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Quadrant 1: Higher or wider?
Quadrant 1: Points - Find their coordinates
Quadrant 1: Making dynamic right-triangles using x(A) and y(B); dynamic rectangles...
Quadrants 4:  What quadrants?
Quadrants 4: Points - Find their coordinates

to:
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August 19, 2008, at 02:18 AM by LFS -
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Rule: The slope of a line doesn't change. It is a number. Parallel lines have the same slope.

to:

Rule: The slope of a line is a number. Parallel lines have the same slope.

August 19, 2008, at 02:17 AM by LFS -
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So: slope is same no matter what points we "pick".
to:
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to:
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  1. Pick any 2 points on the line.
  2. Arbitrarily decide which is the "first point" and "second point".
  3. "change in x" = "x-coordinate of second point" - "x-coordinate of first point".
  4. "change in y" = "y-coordinate of second point" - "y-coordinate of first point".
  5. slope =   \frac{\mbox{change in y}}{\mbox{change in x}}
August 19, 2008, at 02:14 AM by LFS -
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[c]


[c] To calculate the slope we "pick" points on the line A(1,-4) and B(4,2).

to:

[c width=310]


[] To calculate the slope we "pick" points on the line A(1,-4) and B(4,2).

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[row]
[ colspan=2]

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[table border=1 cellpadding=2]
[row]
[c  width=308]


[]This is the same line as above.

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So: slope is same no matter what points we "pick".
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  • Think: slope=speed. Speed is measured distance/time (mph or m/s). Time = x-axis and distance = y-axis.
August 19, 2008, at 01:55 AM by LFS -
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[c]The two points on the line used to "calculate" the slope are A(1,-4) and B(4,2).

We will look "from A to B".
The "change in x" "from A to B" is 4-1=3.
The "change in y" "from A to B" is 2-(-4)=2+4=6.
Slope of this line = m =  \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{6}{3} = 2
to:
August 19, 2008, at 01:42 AM by LFS -
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August 19, 2008, at 01:41 AM by LFS -
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August 19, 2008, at 01:29 AM by LFS -
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August 19, 2008, at 12:56 AM by LFS -
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"change in x" = 0-3 = -3 and "change in y" = -6-0 = -6.
to:
"change in x" = 0-3 = -3 and "change in y" = -6-0 = -6.
August 19, 2008, at 12:53 AM by LFS -
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[tableend]

to:
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August 19, 2008, at 12:49 AM by LFS -
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[ colspan=2]

  • Coordinates of a point are (x,y) so when graphing a point do horizontal then vertical. See&Do

[row]
[ colspan=2]

  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so with slope the vertical change is above the horizontal change in the fraction!

[row]
[ colspan=2]
Think: slope=speed. Speed is measured distance/time (mph or m/s). Time = x-axis and distance = y-axis.
[row]

Changed lines 15-16 from:


[c]The two points on the line used to "calculate" the slope are A(1,-4) and B(4,2).

to:


[c] To calculate the slope we "pick" points on the line A(1,-4) and B(4,2).

Changed lines 20-23 from:
to:
Slope of this line = m =  \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{6}{3} = 2
Changed lines 22-24 from:

Rule: The slope of a line doesn't change. It is a number. Parallel lines have the same slope.

Introduction to Slopes - Money in the Bank

to:
Changed lines 30-42 from:

to:
Deleted lines 43-47:
Changed lines 45-59 from:
to:

[ colspan=2]
Think: slope=speed. Speed is measured distance/time (mph or m/s). Time = x-axis and distance = y-axis.

Changed lines 48-55 from:
to:
Changed lines 63-65 from:
to:
Changed lines 72-82 from:
to:

1. Click on the New point tool. In the drawing pad, find the point with coordinates (1,1) and then click. Point A should be drawn. Check the coordinates of point A by rolling your mouse over it.

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to:
Changed line 76 from:
to:

3. Find the coordinates and draw the points C(5,4) and D(5,1).

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to:

4. Use the Segment tool and make the rectangle ABCD.

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to:
Changed lines 83-85 from:

[tableend]

[table border=1 cellpadding=3 width=100%]

to:
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to:
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Deleted lines 111-126:
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[  width=110px] Global
[]Cartesian Plane

to:
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[]Brief
[]Interactivities involving understanding the slope of a line in the Cartesaian plane.

to:
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[]Grade
[]5-10    Interactivities start at 7th grade level on up

to:

[  width=110px] Global
[]Cartesian Plane

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[]Strand
[]Algebra and Functions / Geometry and Measurement

to:

[]Brief
[]Interactivities involving understanding the slope of a line in the Cartesaian plane.

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[]Standard
[]CA 7AF.3.3

to:

[]Grade
[]5-10    Interactivities start at 7th grade level on up

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[]Keywords
[]line, slope, linear equation, change in y, change in x, ratio

to:

[]Strand
[]Algebra and Functions / Geometry and Measurement

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[]Comments
[]none

to:

[]Standard
[]CA 7AF.3.3

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[]Download
[] 

to:

[]Keywords
[]line, slope, linear equation, change in y, change in x, ratio

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[]Author
[]LFS - contact - website

to:

[]Comments
[]none

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[]Type
[]Freeware - Available for Offline and Online Use - Translatable (html)

to:

[]Download
[] 

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[]Author
[]LFS - contact - website
[row]
[]Type
[]Freeware - Available for Offline and Online Use - Translatable (html)
[row]

August 19, 2008, at 12:33 AM by LFS -
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[c]

to:


[c]The two points on the line used to "calculate" the slope are A(1,-4) and B(4,2).

We will look "from A to B".
The "change in x" "from A to B" is 4-1=3.
The "change in y" "from A to B" is 2-(-4)=2+4=6.
Slope of this line = m = \frac{\mbox{vertical change}}{\mbox{horizontal change}} = \frac{6}{3} = 2
August 19, 2008, at 12:28 AM by LFS -
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to:

August 19, 2008, at 12:26 AM by LFS -
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to:

August 19, 2008, at 12:19 AM by LFS -
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  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so for slope do vertical change then horizontal change.
to:
  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so with slope the vertical change is above the horizontal change in the fraction!
Changed line 27 from:

to:

August 19, 2008, at 12:01 AM by LFS -
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[table border=1 cellpadding=3]
[row]
[ colspan=2]

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[row]
[ colspan=2]

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[row]
[ colspan=2]

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to:

[row]
[c]


[c]
[tableend]  

August 18, 2008, at 11:35 PM by LFS -
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Definition: The slope of a line is the rate of change, that is the: "vertical change"/"horizontal change".

to:

Definition: The slope of a line is the rate of change, that is the: "vertical change"/"horizontal change".

August 18, 2008, at 11:34 PM by LFS -
Changed lines 16-19 from:
  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so for slope do vertical change then horizontal change. Think: slope=speed. Speed is measured distance/time (mph or m/s). Time = x-axis and distance = y-axis.
to:
  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so for slope do vertical change then horizontal change.

Think: slope=speed. Speed is measured distance/time (mph or m/s). Time = x-axis and distance = y-axis.

August 18, 2008, at 11:19 PM by LFS -
Changed line 10 from:

Definition: The slope of a line in the plane is the ratio: "vertical change"/"horizontal change".

to:

Definition: The slope of a line is the rate of change, that is the: "vertical change"/"horizontal change".

Changed line 16 from:
  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so for slope do vertical change then horizontal change.
to:
  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so for slope do vertical change then horizontal change. Think: slope=speed. Speed is measured distance/time (mph or m/s). Time = x-axis and distance = y-axis.
Changed line 21 from:

Rule: The slope of a line is a number (constant) and parallel lines have the same slope.

to:

Rule: The slope of a line doesn't change. It is a number. Parallel lines have the same slope.

August 17, 2008, at 11:28 PM by LFS -
Changed line 14 from:
  • Coordinates of a point are (x,y) so when graphing a point do horizontal then vertical. See&Do
to:
  • Coordinates of a point are (x,y) so when graphing a point do horizontal then vertical. See&Do
August 17, 2008, at 11:27 PM by LFS -
Changed line 14 from:
  • Coordinates of a point are (x,y) so when graphing a point do horizontal then vertical.
to:
  • Coordinates of a point are (x,y) so when graphing a point do horizontal then vertical. See&Do
August 17, 2008, at 11:25 PM by LFS -
Changed lines 14-15 from:
  • The coordinates of a point are (x,y) so when graphing a point do horizontal then vertical.
  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so for slope do vertical change then horizontal change.   
to:
  • Coordinates of a point are (x,y) so when graphing a point do horizontal then vertical.

  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so for slope do vertical change then horizontal change.

  
August 17, 2008, at 11:21 PM by LFS -
Changed line 21 from:

Positive and Negative Slopes - Money in the Bank

to:

Introduction to Slopes - Money in the Bank

August 17, 2008, at 11:21 PM by LFS -
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Changed lines 17-18 from:
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Added lines 20-21:

Positive and Negative Slopes - Money in the Bank

Changed lines 23-25 from:
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Added lines 25-26:
August 17, 2008, at 11:20 PM by LFS -
Changed line 15 from:
  • Slopes are \frac{\mbox{vertical change}}{\mbox{horizontal change}} - so for slope do vertical change then horizontal change.   
to:
  • Slopes are   \frac{\mbox{vertical change}}{\mbox{horizontal change}}   - so for slope do vertical change then horizontal change.   
August 17, 2008, at 11:19 PM by LFS -
Changed line 12 from:
to:
Changed line 15 from:
  • Slopes are \frac{\fgcolor{#990099}{\mbox{vertical change}}}{horizontal change} - so for slope do vertical change then horizontal change.   
to:
  • Slopes are \frac{\mbox{vertical change}}{\mbox{horizontal change}} - so for slope do vertical change then horizontal change.   
August 17, 2008, at 11:14 PM by LFS -
August 17, 2008, at 11:13 PM by LFS -
Changed line 10 from:

Definition: The slope of a line in the plane is the ratio: "vertical change"/"horizontal change".  

to:

Definition: The slope of a line in the plane is the ratio: "vertical change"/"horizontal change".

Added lines 12-17:
August 17, 2008, at 10:44 PM by LFS -
Changed line 12 from:

Rule: The slope of every line is a constant and parallel lines have the same slope.

to:

Rule: The slope of a line is a number (constant) and parallel lines have the same slope.

August 16, 2008, at 10:13 AM by LFS -
Changed line 138 from:
to:
August 16, 2008, at 10:10 AM by LFS -
Added lines 14-15:

Positive and Negative Slopes - Money in the Bank

August 16, 2008, at 09:19 AM by LFS -
Changed line 3 from:

Mathcasts         Examples      Practice    More      [[glossary/S]

to:

Mathcasts         Examples      Practice    More      S

Changed line 10 from:

Definition: The slope of a line in the plane is the ratio: "vertical change"/"horizontal change".  

to:

Definition: The slope of a line in the plane is the ratio: "vertical change"/"horizontal change".  

August 16, 2008, at 09:17 AM by LFS -
Added lines 1-171:


Page last modified on February 04, 2009, at 03:44 AM