Question

a line has a slope of -\frac{1}{3} and passes through the point (5, 0). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know $m=-\frac{1}{3}$, so the equation becomes $y =-\frac{1}{3}x + b$.

Step2: Substitute the point into the equation

Substitute the point $(x = 5,y = 0)$ into $y=-\frac{1}{3}x + b$. We get $0=-\frac{1}{3}(5)+b$.

Step3: Solve for $b$

First, simplify the right - hand side: $0=-\frac{5}{3}+b$. Then add $\frac{5}{3}$ to both sides of the equation. So $b=\frac{5}{3}$.

Step4: Write the final equation

Substitute $b = \frac{5}{3}$ back into $y=-\frac{1}{3}x + b$. The equation of the line in slope - intercept form is $y=-\frac{1}{3}x+\frac{5}{3}$.

Answer:

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