Question

Find an equation of the line between (-4,2) and (1,-8)

Answer 1

The formula to calculate the equation of a line between two points is,

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

Given

$\begin{gathered} (x_1,y_1)\rightarrow(-4,2) \\ (x_2,y_2)\rightarrow(1,-8) \end{gathered}$

Therefore,

$\frac{y-2}{x--4}=\frac{-8-2}{1--4}$

Simplify

$\begin{gathered} \frac{y-2}{x+4}=\frac{-10}{1+4} \\ \frac{y-2}{x+4}=-\frac{10}{5} \\ \frac{y-2}{x+4}=-2 \\ \text{Cross}-m\text{ultiply} \\ y-2=-2(x+4) \\ y=-2(x+4)+2=-2x-8+2=-2x-6 \\ \therefore y=-2x-6 \end{gathered}$

Hence, the equation of the line is

$y=-2x-6$