Question

a line that includes the point (4, -2) has a slope of 9. what is its equation in point - slope form?
use the specified point in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.

Explanation:

Step1: Recall point - slope formula

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

Step2: Identify values of $x_1$, $y_1$ and $m$

We are given that the point $(x_1,y_1)=(4,-2)$ and the slope $m = 9$.

Step3: Substitute values into the formula

Substitute $x_1 = 4$, $y_1=-2$ and $m = 9$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y-(-2)=9(x - 4)$.
Simplify the left - hand side: $y + 2=9(x - 4)$.

Answer:

$y + 2=9(x - 4)$