Question

find an equation for the line below.

Explanation:

Step1: Identify two points

Let the two points on the line be $(-6, - 2)$ and $(4,-6)$.

Step2: Calculate the slope $m$

Use the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-6,y_1 = - 2,x_2=4,y_2=-6$. So $m=\frac{-6-( - 2)}{4-( - 6)}=\frac{-6 + 2}{4 + 6}=\frac{-4}{10}=-\frac{2}{5}$.

Step3: Use the point - slope form $y - y_1=m(x - x_1)$

Using the point $(-6,-2)$ and $m =-\frac{2}{5}$, we have $y-(-2)=-\frac{2}{5}(x - (-6))$.

Step4: Simplify the equation

$y + 2=-\frac{2}{5}(x + 6)$
$y+2=-\frac{2}{5}x-\frac{12}{5}$
$y=-\frac{2}{5}x-\frac{12}{5}-2$
$y=-\frac{2}{5}x-\frac{12 + 10}{5}$
$y=-\frac{2}{5}x-\frac{22}{5}$

Answer:

$y =-\frac{2}{5}x-\frac{22}{5}$