# How do you find the x and y intercepts for -3x+4y=8?

Dec 21, 2015

Substitute in $0$ for $x$ or $y$ to find that there is
an $x$-intercept at $\left(- \frac{8}{3} , 0\right)$ and
a $y$-intercept at $\left(0 , 2\right)$

#### Explanation:

An $x$-intercept of a graph occurs when the graph meets the $x$-axis, that is, at a point where $y = 0$. Similarly, a $y$-intercept occurs where $x = 0$.

To find the $x$ and $y$ intercepts, then, we simply substitute in $0$ for $y$ and $x$ respectively.

Substituting $0$ for $y$ gives us

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

$\implies - 3 x = 8$

$\implies x = - \frac{8}{3}$

Thus the $x$-intercept occurs at $\left(- \frac{8}{3} , 0\right)$.

Substituting $0$ for $x$ gives us

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

$\implies 4 y = 8$

$\implies y = 2$

So the $y$-intercept occurs at $\left(0 , 2\right)$