# How do you find the x and y intercept of 8x − 3y = −21?

Mar 24, 2017

See the entire solution process below:

#### Explanation:

To find the intercepts by substitution we must do the following:

y-intercept - substitute $0$ for $x$ and solve for $y$:

$8 x - 3 y = - 21$ becomes:

$\left(8 \times 0\right) - 3 y = - 21$

$0 - 3 y = - 21$

$- 3 y = - 21$

$\frac{- 3 y}{\textcolor{red}{- 3}} = \frac{- 21}{\textcolor{red}{- 3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} y}{\cancel{\textcolor{red}{- 3}}} = 7$

$y = 7$

The y-intercept is $7$ or $\left(0 , 7\right)$

x-intercept - substitute $0$ for $y$ and solve for $x$:

$8 x - 3 y = - 21$ becomes:

$8 x - \left(3 \times 0\right) = - 21$

$8 x - 0 = - 21$

$8 x = - 21$

$\frac{8 x}{\textcolor{red}{8}} = \frac{- 21}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} x}{\cancel{\textcolor{red}{8}}} = - \frac{21}{8}$

$x = - \frac{21}{8}$

The x-intercept is $- \frac{21}{8}$ or $\left(- \frac{21}{8} , 0\right)$