Question

what is the equation of the line that passes through the point (-1, 5) and has a slope of -3?

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation 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: Substitute the values

We are given that $x_1=-1$, $y_1 = 5$ and $m=-3$. Substituting these values into the point - slope form, we get:
$y - 5=-3(x - (-1))$
Simplify the right - hand side: $y - 5=-3(x + 1)$

Step3: Convert to slope - intercept form (optional, but to get the equation in a more familiar form)

Expand the right - hand side: $y - 5=-3x-3$
Add 5 to both sides of the equation: $y=-3x - 3+5$
Simplify the constants: $y=-3x + 2$
We can also leave it in point - slope form, but the slope - intercept form is a common way to present the equation of a line.

Answer:

The equation of the line is $y=-3x + 2$ (or in point - slope form $y - 5=-3(x + 1)$)