# What are the intercepts of 5x+3y=13?

Feb 17, 2017

The y-intercept is $\frac{13}{3}$ or $\left(0 , \frac{13}{3}\right)$

The x-intercept is $\frac{13}{5}$ or $\left(\frac{13}{5} , 0\right)$

#### Explanation:

Using the cover-up method we will solve for the y-intercept by eliminating the $x$ term and solving for $y$;

$3 y = 13$

$\frac{3 y}{\textcolor{red}{3}} = \frac{13}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} y}{\cancel{\textcolor{red}{3}}} = \frac{13}{3}$

$y = \frac{13}{3}$

Therefore the y-intercept is $\frac{13}{3}$ or $\left(0 , \frac{13}{3}\right)$

Using the cover-up method we will solve for the x-intercept by eliminating the $y$ term and solving for $x$;

$5 x = 13$

$\frac{5 x}{\textcolor{red}{5}} = \frac{13}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} = \frac{13}{5}$

$x = \frac{13}{5}$

Therefore the x-intercept is $\frac{13}{5}$ or $\left(\frac{13}{5} , 0\right)$