# How do you find the x and y intercepts of y=2/3x-4?

Mar 1, 2017

See the entire solution process below:

#### Explanation:

To find the y-intercept by substitution, substitute $0$ for $x$ and calculate $y$:

$y = \left(\frac{2}{3} \times 0\right) - 4$

$y = 0 - 4$

$y = - 4$ Therefore the y-intercept is $- 4$ or $\left(0 , - 4\right)$

To find the x-intercept by substitution, substitute $0$ for $y$ and solve for $x$:

$0 = \frac{2}{3} x - 4$

$0 + \textcolor{red}{4} = \frac{2}{3} x - 4 + \textcolor{red}{4}$

$4 = \frac{2}{3} x - 0$

$4 = \frac{2}{3} x$

$\frac{\textcolor{red}{3}}{\textcolor{b l u e}{2}} \times 4 = \frac{\textcolor{red}{3}}{\textcolor{b l u e}{2}} \times \frac{2}{3} x$

$\frac{12}{\textcolor{b l u e}{2}} = \frac{\cancel{\textcolor{red}{3}}}{\cancel{\textcolor{b l u e}{2}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{2}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} x$

$6 = x$

$x = 6$ Therefore the x-intercept is $6$ or $\left(6 , 0\right)$