# How to determine if an equation is linear or not

In this video lesson, we are going to learn how to determine if an equation is linear or not by giving the definition of a linear equation.

• Give a rule that relates $x$ and $y$ in the following ordered pairs:

a. $\{(-2,2),(-1,1),(0,0),(1,-1),(2,-2)\}$

b. $\{(1,2),(2,3),(4,5)\}$

• A linear equation in two variables is an equation that can be written in the form

$Ax + By = C$

where $A,B$ and $C$ are real numbers, $A$ and $B$ not both zero.

This means that for an equation to be linear, the following must be satisfied:

a.  The exponents of x and y must be both 1.

b.  The variables must not appear in the denominator

c.  No square roots, cube roots, etc. for the variables

• Which of the following are linear  equations in two variables?

1.  $2x + 5y = 4$

2.  $x^2 + 4y = 5$

3.  $3x - 4 = 7y$

4.  $x = 5$

5. $\displaystyle{\frac{4}{5}}y - 3=2x$

6.  $\displaystyle{\frac{4}{2x}} + 3y=-4$

• Which of the following are linear equations in two variables?

a. $y^2=y+3-4x$

b. $\displaystyle{\frac{x-4}{2}}=-6y+3$

c.  $\displaystyle{x=\frac{1}{y}}$