# How do you find the x- and y-intercept of the line 4x – 7y = 84?

Apr 21, 2017

See the entire solution process below:

#### Explanation:

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

$4 x - 7 y = 84$ becomes:

$\left(4 \cdot 0\right) - 7 y = 84$

$0 - 7 y = 84$

$- 7 y = 84$

$\frac{- 7 y}{\textcolor{red}{- 7}} = \frac{84}{\textcolor{red}{- 7}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 7}}} y}{\cancel{\textcolor{red}{- 7}}} = - 12$

$y = - 12$

The y-intercept is $- 12$ or $\left(0 , - 12\right)$

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

$4 x - 7 y = 84$ becomes:

$4 x - \left(7 \cdot 0\right) = 84$

$4 x - 0 = 84$

$4 x = 84$

$\frac{4 x}{\textcolor{red}{4}} = \frac{84}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} = 21$

$x = 21$

The x-intercept is $21$ or $\left(21 , 0\right)$