Question

a line has a slope of $\frac{1}{3}$ and passes through the point (-5, -5). what is its equation in point - slope form? use the specified point in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.

Explanation:

Step1: Recall point - slope formula

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.

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

Given $m=\frac{1}{3}$, $x_1=-5$ and $y_1 = - 5$.

Step3: Substitute values into formula

Substitute into $y - y_1=m(x - x_1)$: $y-(-5)=\frac{1}{3}(x - (-5))$.

Step4: Simplify the equation

$y + 5=\frac{1}{3}(x + 5)$.

Answer:

$y + 5=\frac{1}{3}(x + 5)$