Question

a line has a slope of 7 and passes through the point (-1, -8). write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. We know that $m = 7$ and the point $(x_1,y_1)=(-1,-8)$. Substitute these values into the point - slope form:
$y-(-8)=7(x - (-1))$
Simplify the left - hand side and the right - hand side: $y + 8=7(x + 1)$

Step2: Expand and convert to slope - intercept form

Slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.
Expand the right - hand side of $y + 8=7(x + 1)$:
$y+8 = 7x+7$
Subtract 8 from both sides to solve for $y$:
$y=7x + 7-8$
$y=7x-1$

Answer:

$y = 7x-1$