# How do you find the x and y intercepts for 2x - y = 8?

Apr 9, 2017

x-intercept: $4$
y-intercept: $- 8$

#### Explanation:

The x-intercept is the value of $x$ where the equation crosses the X-axis; that is it is the value of $x$ when $y = 0$.
Substituting $0$ for $y$ in $2 x - y = 8$
$\textcolor{w h i t e}{\text{XXX")2x-0=8color(white)("xxx")rarrcolor(white)("xxx}} x = 4$
[Some instructors prefer to have the intercept written as as a coordinate pair; in this case, the coordinates for the x-intercept would be $\left(4 , 0\right)$].

Similary, the y-intercept is the value of $y$ when $x = 0$.
Substituting $0$ for $x$ in $2 x - y = 8$
$\textcolor{w h i t e}{\text{XXX")2 * 0 -y =8 color(white)("xxx")rarrcolor(white)("xxx}} y = - 8$
[...or, given as a coordinate pair: $\left(0 , - 8\right)$].

Apr 9, 2017

See the entire solution process below:

#### Explanation:

To find the $y$ intercept, set $x$ equal to $0$ and solve for $y$:

$2 x - y = 8$ becomes:

$\left(2 \cdot 0\right) - y = 8$

$0 - y = 8$

$- y = 8$

$\textcolor{red}{- 1} \cdot - y = \textcolor{red}{- 1} \cdot 8$

$y = - 8$

The y-intercept is $- 8$ or $\left(0 , - 8\right)$

To find the $x$ intercept, set $y$ equal to $0$ and solve for $x$:

$2 x - y = 8$ becomes:

$2 x - 0 = 8$

$2 x = 8$

$\frac{2 x}{\textcolor{red}{2}} = \frac{8}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = 4$

$x = 4$

The x-intercept is $4$ or $\left(4 , 0\right)$