Question

find an equation of the line containing the given pair of points. (-5, -6) and (-9, -4)
the equation of the line in slope - intercept form is y = . (simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-5,-6)$ and $(x_2,y_2)=(-9,-4)$. Then $m=\frac{-4-(-6)}{-9 - (-5)}=\frac{-4 + 6}{-9+5}=\frac{2}{-4}=-\frac{1}{2}$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form $y=mx + b$. Let's use the point $(-5,-6)$ and $m =-\frac{1}{2}$.
$y-(-6)=-\frac{1}{2}(x - (-5))$
$y + 6=-\frac{1}{2}(x + 5)$
$y+6=-\frac{1}{2}x-\frac{5}{2}$
$y=-\frac{1}{2}x-\frac{5}{2}-6$
$y=-\frac{1}{2}x-\frac{5}{2}-\frac{12}{2}$
$y=-\frac{1}{2}x-\frac{17}{2}$

Answer:

$y =-\frac{1}{2}x-\frac{17}{2}$