# How do you find the equation, x-intercept, and the y-intercept for the line with an y-intercept of 5 and a slope of -1/3?

Apr 13, 2017

See the entire solution process below:

#### Explanation:

We can use the slope intercept formula to write the equation of the line. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

Substituting the information from the problem gives:

$y = \textcolor{red}{- \frac{1}{3}} x + \textcolor{b l u e}{5}$

The y-intercept was given as part of the problem: $\textcolor{b l u e}{b = 5}$ or $\left(0 , 5\right)$

To find the x-intercept we set $y$ equal to $0$ and solve for $x$:

$y = \textcolor{red}{- \frac{1}{3}} x + \textcolor{b l u e}{5}$ becomes:

$0 = \textcolor{red}{- \frac{1}{3}} x + \textcolor{b l u e}{5}$

$0 - 5 = \textcolor{red}{- \frac{1}{3}} x + \textcolor{b l u e}{5} - 5$

$- 5 = \textcolor{red}{- \frac{1}{3}} x + 0$

$- 5 = \textcolor{red}{- \frac{1}{3}} x$

$- 3 \times - 5 = - 3 \times \textcolor{red}{- \frac{1}{3}} x$

$15 = \textcolor{red}{\cancel{\textcolor{b l a k c}{- 3}}} \times \cancel{\textcolor{red}{- \frac{1}{3}}} x$

$15 = x$

The x-intercept is $15$ or $\left(15 , 0\right)$