Question

find an equation of the line containing the given pair of points.
(-2, -6) and (-8, -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 formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Let $(x_1,y_1)=(-2,-6)$ and $(x_2,y_2)=(-8,-4)$.
$m=\frac{-4-(-6)}{-8-(-2)}=\frac{2}{-6}=-\frac{1}{3}$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=-\frac{1}{3}$ and $(x,y)=(-2,-6)$.
$-6 = -\frac{1}{3}(-2) + b$
$-6 = \frac{2}{3} + b$
$b = -6 - \frac{2}{3} = -\frac{18}{3} - \frac{2}{3} = -\frac{20}{3}$

Step3: Write line equation

Substitute $m=-\frac{1}{3}$ and $b=-\frac{20}{3}$ into $y=mx+b$.

Answer:

$y = -\frac{1}{3}x - \frac{20}{3}$