# How do you find the x and y-intercept for the equation: 4x - 3y - 6 = 0#?

Jan 18, 2018

See a solution process below:

#### Explanation:

x-intercept: Set $y$ to $0$ and solve for $x$:

$4 x - 3 y - 6 = 0$ becomes:

$4 x - \left(3 \cdot 0\right) - 6 = 0$

$4 x - 0 - 6 = 0$

$4 x - 6 = 0$

$4 x - 6 + \textcolor{red}{6} = 0 + \textcolor{red}{6}$

$4 x - 0 = 6$

$4 x = 6$

$\frac{4 x}{\textcolor{red}{4}} = \frac{6}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} = \frac{6}{4}$

$x = \frac{3}{2}$

The x-intercept is: $x = \frac{3}{2}$ or $\left(\frac{3}{2} , 0\right)$

y-intercept: Set $x$ to $0$ and solve for $y$:

$4 x - 3 y - 6 = 0$ becomes:

$\left(4 \cdot 0\right) - 3 y - 6 = 0$

$0 - 3 y - 6 = 0$

$- 3 y - 6 = 0$

$- 3 y - 6 + \textcolor{red}{6} = 0 + \textcolor{red}{6}$

$- 3 y - 0 = 6$

$- 3 y = 6$

$\frac{- 3 y}{\textcolor{red}{- 3}} = \frac{6}{\textcolor{red}{- 3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} y}{\cancel{\textcolor{red}{- 3}}} = \frac{6}{-} 3$

$y = - 2$

The y-intercept is: $y = - 2$ or $\left(0 , - 2\right)$