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=(20)/(6)=(10)/(3) \\ \\ 10=4m+b \\ 10=(40)/(3)+b \\ b=10-(40)/(3) \\ b=-(10)/(3) \end{gathered}`

So our equation is:

`y=(10)/(3)x-(10)/(3)`