Question

A line passes though the points (-5,-4) and (7,-7) . What is it’s equation in point-slope form?

Answer 1

Given the points of the line

$(-5,-4)\text{and(7,-7)}$

To find the equation of the line in point-slope form, we will follow the steps below

Step 1:

$\text{slope}=m=\frac{-7-(-4)}{7-(-5)}=\frac{-7+4}{7+5}=\frac{-3}{12}=-\frac{1}{4}$

The equation of the line in point-slope form is given by

$\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ m=-\frac{1}{4} \\ x_1=-5 \\ y_1=-4 \end{gathered}$

Substituting these values, the point-slope form of the line will be:

$\begin{gathered} y-(-4)=-\frac{1}{4}(x-(-5)) \\ y+4=-\frac{1}{4}(x+5) \end{gathered}$