Question

question
what is the equation of the line that passes through the point (-1, 4) and has a slope of -5?

Explanation:

Step1: Recall point - slope form

The point - slope form of a line 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 $x_1=- 1$, $y_1 = 4$ and $m=-5$. Substituting these values into the point - slope form, we get:
$y - 4=-5(x - (-1))$
Simplify the right - hand side: $y - 4=-5(x + 1)$

Step3: Convert to slope - intercept form (optional, but common)

Expand the right - hand side: $y-4=-5x-5$
Add 4 to both sides of the equation: $y=-5x-5 + 4$
Simplify the right - hand side: $y=-5x-1$

Answer:

The equation of the line is $y=-5x - 1$ (or in point - slope form $y - 4=-5(x + 1)$)