Question

Consider the three points, (3,7),(-6,1) and (9,y) on the same line. Find the value of y and explain your steps.

Answer 1

let us find the slope using 2 points

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1-7}{-6-3} \\ m=\frac{-6}{-9} \\ m=\frac{2}{3} \end{gathered}$

Therefore let us find y

$\begin{gathered} \frac{2}{3}=\frac{y-1}{9+6} \\ \frac{2}{3}=\frac{y-1}{15} \\ \text{cross multiply} \\ 30=3(y-1) \\ 30=3y-3 \\ 33=3y \\ y=\frac{33}{3} \\ y=11 \end{gathered}$