# How do you find the x and y intercept of 4x-3y+8=0?

May 1, 2017

See the solution process below:

#### Explanation:

For the x-intercept:

Substitute $0$ for $y$ and solve for $x$:

$4 x - 3 y + 8 = 0$ becomes:

$4 x - \left(3 \cdot 0\right) + 8 = 0$

$4 x - 0 + 8 = 0$

$4 x + 8 = 0$

$4 x + 8 - \textcolor{red}{8} = 0 - \textcolor{red}{8}$

$4 x + 0 = - 8$

$4 x = - 8$

$\frac{4 x}{\textcolor{red}{4}} = - \frac{8}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} = - 2$

$x = - 2$

The x-intercept is $- 2$ or $\left(- 2 , 0\right)$

For the y-intercept:

Substitute $0$ for $x$ and solve for $y$:

$4 x - 3 y + 8 = 0$ becomes:

$\left(4 \cdot 0\right) - 3 y + 8 = 0$

$0 - 3 y + 8 = 0$

$- 3 y + 8 = 0$

$- 3 y + 8 - \textcolor{red}{8} = 0 - \textcolor{red}{8}$

$- 3 y + 0 = - 8$

$- 3 y = - 8$

$\frac{- 3 y}{\textcolor{red}{- 3}} = \frac{- 8}{\textcolor{red}{- 3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} y}{\cancel{\textcolor{red}{- 3}}} = \frac{8}{3}$

$y = \frac{8}{3}$

The y-intercept is $\frac{8}{3}$ or $\left(0 , \frac{8}{3}\right)$