Question

what is the equation of the line that passes through the point (-3,7) and has a slope of - 1?

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 given values

Here, $x_1=-3$, $y_1 = 7$ and $m=-5$. Substituting these into the point - slope form gives $y - 7=-5(x-(-3))$.

Step3: Simplify the equation

$y - 7=-5(x + 3)$. Expand the right - hand side: $y-7=-5x-15$. Then, add 7 to both sides to get the slope - intercept form: $y=-5x-8$.

Answer:

$y=-5x - 8$