# How do you find the x and y intercepts of 8y-5=3x?

Jan 18, 2017

See the entire solution process below:

#### Explanation:

To find the x-intercept we set $\textcolor{red}{y}$ to $\textcolor{red}{0}$ and solve for $x$:

$8 \textcolor{red}{y} - 5 = 3 x$ becomes:

$\left(8 \times \textcolor{red}{0}\right) - 5 = 3 x$

$0 - 5 = 3 x$

$- 5 = 3 x$

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

$- \frac{5}{3} = x$

$x = - \frac{5}{3}$

To find the y-intercept we set $\textcolor{red}{x}$ to $\textcolor{red}{0}$ and solve for $y$:

$8 y - 5 = 3 \textcolor{red}{x}$ becomes:

$8 y - 5 = \left(3 \times \textcolor{red}{0}\right)$

$8 y - 5 = 0$

$8 y - 5 + \textcolor{red}{5} = 0 + \textcolor{red}{5}$

$8 y - 0 = 5$

$\frac{8 y}{\textcolor{red}{8}} = \frac{5}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} y}{\cancel{\textcolor{red}{8}}} = \frac{5}{8}$

$y = \frac{5}{8}$

The x-intercept is $- \frac{5}{3}$ or $\left(- \frac{5}{3} , 0\right)$

The y-intercept is $\frac{5}{8}$ or $\left(0 , \frac{5}{8}\right)$