Question

use point - slope form to write the equation of a line that passes through the point (-13, -11) with slope $-\frac{1}{5}$.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.

Step2: Identify values of $x_1,y_1$ and $m$

We are given that the point $(x_1,y_1)=(- 13,-11)$ and the slope $m =-\frac{1}{5}$.

Step3: Substitute values into the formula

Substitute $x_1=-13$, $y_1 = - 11$ and $m=-\frac{1}{5}$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y-(-11)=-\frac{1}{5}(x - (-13))$.
Simplify the left - hand side and the right - hand side:
The left - hand side $y-(-11)=y + 11$.
The right - hand side $-\frac{1}{5}(x - (-13))=-\frac{1}{5}(x + 13)$.
So the equation in point - slope form is $y + 11=-\frac{1}{5}(x + 13)$.

Answer:

The equation of the line in point - slope form is $y + 11=-\frac{1}{5}(x + 13)$