For an equation to be linear, the slope has to be the same/constant.
To find the slope (m), you use the slope formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] and substitute in 2 points
(1 , 60) [x₁ , y₁] and (5 , 70) [x₂ , y₂]
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{70-60}{5-1}[/tex]
[tex]m=\frac{10}{4} =\frac{5}{2}[/tex] or 2.5
Try a different point to see if the slope is the same:
(5, 70) and (20, 80)
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{80-70}{20-5}[/tex]
[tex]m=\frac{10}{15} =\frac{2}{3}[/tex] or 0.6666666
Since the slopes are different, a linear equation can not be used
