what is the equation of the line that passes through the point (3, -7) and has a slope of -2?

Explanation:

Step1: Recall point - slope form

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

Step2: Substitute values

Given $(x_1,y_1)=(3,-7)$ and $m = - 2$, substitute into the point - slope form: $y-(-7)=-2(x - 3)$.

Step3: Simplify the equation

$y + 7=-2x+6$.

Step4: Rewrite in slope - intercept form

Subtract 7 from both sides: $y=-2x+6 - 7$, so $y=-2x - 1$.

Answer:

$y=-2x - 1$