# How do you determine the intercepts of y=5x-13?

Dec 26, 2016

The y-intercept is: -13 or (0, -13).

The x-intercept is 13/5 or (13/5, 0)

#### Explanation:

Because this equation is in the slope-intercept form $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and and $\textcolor{b l u e}{b}$ is the y-intercept we know for this equation the y-intercept is: -13 or (0, 13).

To find the $x$ intercept we need to set $y = 0$ and solve for $x$:

$0 = 5 x - 13$

$0 + \textcolor{red}{13} = 5 x - 13 + \textcolor{red}{13}$

$13 = 5 x - 0$

$13 = 5 x$

$\frac{13}{\textcolor{b l u e}{5}} = \frac{5 x}{\textcolor{b l u e}{5}}$

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

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

Therefore the x-intercept is 13/5 or (13/5, 0)