Question

a line passes through the point (1, -8) and has a slope of -9. write an equation in point - slope form for this line.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a line is given by $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.

Step2: Identify values

We are given that the point $(x_1,y_1)=(1, - 8)$ and the slope $m=-9$.

Step3: Substitute values into formula

Substitute $x_1 = 1$, $y_1=-8$ and $m = - 9$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y-(-8)=-9(x - 1)$, which simplifies to $y + 8=-9(x - 1)$.

Answer:

$y + 8=-9(x - 1)$