Question

(4,10)(-2,-10) what is the linear equation

Answer 1

Using the slope-intercept form of the linear equation and the points given, we have:

$\begin{gathered} y=mx+b_{} \\ (4,10)\colon \\ 10=4m+b \\ (-2,-10)\colon \\ -10=-2m+b \end{gathered}$

Subtracting the 1st and 2nd equations, we have:

$\begin{gathered} 10-(-10)=4m+b-(-2m+b) \\ 10+10=4m+b+2m-b \\ 20=6m \\ m=\frac{20}{6}=\frac{10}{3} \\ \\ 10=4m+b \\ 10=\frac{40}{3}+b \\ b=10-\frac{40}{3} \\ b=-\frac{10}{3} \end{gathered}$

So our equation is:

$y=\frac{10}{3}x-\frac{10}{3}$