Question

what is an equation of the line that passes through the points (-2,7) and (-8,4)?

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-2,7)$ and $(x_2,y_2)=(-8,4)$. Then $m=\frac{4 - 7}{-8-(-2)}=\frac{-3}{-6}=\frac{1}{2}$.

Step2: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(-2,7)$ and $m = \frac{1}{2}$, we have $y - 7=\frac{1}{2}(x+2)$.

Step3: Convert to slope - intercept form

Expand the right side: $y - 7=\frac{1}{2}x + 1$. Then add 7 to both sides to get $y=\frac{1}{2}x+8$.

Answer:

$y=\frac{1}{2}x + 8$