Question

a line has a slope of $-\frac{1}{7}$ and passes through the point $(-7, -10)$. 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 $m =-\frac{1}{7}$ and the point $(x_1,y_1)=(-7,-10)$.
Substitute these values into the point - slope form:
$y-(-10)=-\frac{1}{7}(x - (-7))$
Simplify the left - hand side and the right - hand side:
$y + 10=-\frac{1}{7}(x + 7)$

Step2: Convert to slope - intercept form

The slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We need to simplify the equation $y + 10=-\frac{1}{7}(x + 7)$ to get it in the form $y=mx + b$.
First, distribute the $-\frac{1}{7}$ on the right - hand side:
$y+10=-\frac{1}{7}x-1$
Then, subtract 10 from both sides of the equation to solve for $y$:
$y=-\frac{1}{7}x-1 - 10$
$y=-\frac{1}{7}x-11$

Answer:

$y =-\frac{1}{7}x-11$