Question

what is an equation of the line that passes through the points (-4, -5) and (-8, -2)?

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-4,-5)$ and $(x_2,y_2)=(-8,-2)$. Then $m=\frac{-2-(-5)}{-8 - (-4)}=\frac{-2 + 5}{-8+4}=\frac{3}{-4}=-\frac{3}{4}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-4,-5)$ and $m =-\frac{3}{4}$, we have $y-(-5)=-\frac{3}{4}(x - (-4))$, which simplifies to $y + 5=-\frac{3}{4}(x + 4)$.

Step3: Convert to slope - intercept form

Expand the right side: $y+5=-\frac{3}{4}x-3$. Then subtract 5 from both sides to get $y=-\frac{3}{4}x-8$.

Answer:

$y =-\frac{3}{4}x - 8$