a line passes through the points (-4, 9) and (4, -15). write its equation in slope - intercept form. write…

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-4,9)$ and $(x_2,y_2)=(4,-15)$. $m=\frac{-15 - 9}{4-(-4)}=\frac{-24}{8}=-3$.

Step2: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(-4,9)$ and $m = - 3$, we have $y - 9=-3(x+4)$.

Step3: Simplify to slope - intercept form

Expand the right side: $y - 9=-3x-12$. Add 9 to both sides: $y=-3x-12 + 9$. So, $y=-3x-3$.

Answer:

$y=-3x - 3$