Question

Write the equation of the line that passes through the points (-4,3) and (-8,8). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answer 1

We have to use the slope formula first

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's replace the given points

$m=\frac{8-3}{-8-(-4)}=\frac{5}{-8+4}=-\frac{5}{4}$

Then, we use the point-slope formula to find the equation

$y-y_1=m(x-x_1)$

Let's replace a point and the slope,

$\begin{gathered} y-3=-\frac{5}{4}(x-(-4) \\ y-3=-\frac{5}{4}(x+4) \\ y=-\frac{5}{4}x-5+3 \\ y=-\frac{5}{4}x-2 \end{gathered}$

Hence, the equation is

$y=-\frac{5}{4}x-2$