Notice: 1 variable: point on line, 2 variables: line in plane, 3 variables: plane in space.
Regulations: A linear function is a linear equation in two variables. (The graph of a linear function is a line.)
Is it a linear equation? Examples
Regulation a: All the variables in a linear equation are "on top" (in the numerator of any fraction).
Regulation b: No two variables in a linear equation are "together" (multiplied).
Regulation c: A linear equation has no exponents (except 1) or roots on the variables.
Regulation d: A linear equation is an equation.
No, the variable x is in the denominator. a
No, the variables x and y are multiplied. b
Yes, usually the letters a , b and c represent constants (numbers) and not variables. Teachers usually use letters from the beginning of the alphabet to mean constants A, B, C, D, .... and a, b, c, d, ... and letters from the end of the alphabet to be variables. When in doubt - ASK! Your teacher must be clear on this or it isn't fair!
No, this is an expression - NOT an equation. d
No, the variable x has an exponent of 2. c
Yes, it doesn't matter that the numbers are ugly (rationals and irrationals), the variables t and w are "clean".
No, the variable x is inside a square root. c
Mathematically speaking No, because the variable x is in the denominator. BUT, your teacher may say it is linear, because it can be made into a linear equation by multiplying both sides by x . This is different than example 1 because that example is not linear no matter what.