# What are the intercepts of -31x-4y=9?

Feb 9, 2017

To find the intercepts you need to set the other variable to $0$ and solve for the intercept variable you are looking for:

Solution for y-intercept - set $x = 0$ and solve for $y$:

$\left(- 31 \times 0\right) - 4 y = 9$

$0 - 4 y = 9$

$- 4 y = 9$

$\frac{- 4 y}{\textcolor{red}{- 4}} = \frac{9}{\textcolor{red}{- 4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 4}}} y}{\cancel{\textcolor{red}{- 4}}} = - \frac{9}{4}$

$y = - \frac{9}{4}$; y-intercept is $- \frac{9}{4}$ or $\left(0. - \frac{9}{4}\right)$

Solution for x-intercept - set $y = 0$ and solve for $x$:

$- 31 x - \left(4 \times 0\right) = 9$

$- 31 x - 0 = 9$

$- 31 x = 9$

$\frac{- 31 x}{\textcolor{red}{- 31}} = \frac{9}{\textcolor{red}{- 31}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 31}}} x}{\cancel{\textcolor{red}{- 31}}} = - \frac{9}{31}$

$x = - \frac{9}{31}$; x-intercept is $- \frac{9}{31}$ or $\left(- \frac{9}{31} , 0\right)$