Identifying Equations as Linear and Nonlinear

Use definitions of linear equations to determine if equations are linear or nonlinear.


Formula of Slope: \frac{y_2=y_1}{x_2=x_1}

Note: If the slope is constant, the equation is linear.

Examples: 

 

Example 1


Determine if y=3x^2+2 is linear

X Y
2 14
0 2
-1 5
-2 14
Slope
\frac{14-2}{2-0}=6
\frac{2-5}{0-(-1)}=-3
\frac{5-14}{-1-2}=6

Solution: The equation is not linear. The slope is not consistent

Example 2


Determine if y=5x+3

X Y
2 13
0 18
3 5
1 8
Slope
\frac{13-3}{2-0}=5
\frac{3-18}{0-3)}=5
\frac{18-8}{3-1}=5

 

Solution: The equation is Linear.The slope is consistent