what is the equation of the line that passes through the point (-3, 6) and has a slope of -4?

Explanation:

Step1: Use 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. Here, $x_1=-3$, $y_1 = 6$ and $m=-4$. Substitute these values into the formula: $y - 6=-4(x-(-3))$.

Step2: Simplify the equation

First, simplify $x-(-3)$ to $x + 3$. So we have $y-6=-4(x + 3)$. Expand the right - hand side: $y-6=-4x-12$. Then, add 6 to both sides of the equation to get it in slope - intercept form $y=mx + b$. $y=-4x-12 + 6$. $y=-4x-6$.

Answer:

$y=-4x - 6$