Question

which equation represents a line that passes through (-9, -3) and has a slope of -6?

$y - 9 = -6(x - 3)$

$y + 3 = -6(x + 9)$

$y + 9 = -6(x + 3)$

$y - 3 = -6(x - 9)$

Explanation:

Step1: Recall point - slope form

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 $x_1,y_1$ and $m$

We are given that the line passes through the point $(-9,-3)$, so $x_1=-9$ and $y_1 = - 3$. The slope $m=-6$.

Step3: Substitute into point - slope form

Substitute $x_1=-9$, $y_1=-3$ and $m = - 6$ into the point - slope form $y - y_1=m(x - x_1)$.
We get $y-(-3)=-6(x - (-9))$.
Simplifying the left - hand side and the right - hand side: $y + 3=-6(x + 9)$.

Answer:

$y + 3=-6(x + 9)$