# How do you find the x and y intercept of 4x+8y=12?

Jan 7, 2017

Y int at $\left(0 , \frac{3}{2}\right)$
X int at $\left(3 , 0\right)$

#### Explanation:

The line is easier to visualize when the equation is in slope-intercept form:
$4 x + 8 y = 12$

Divide each side by 4:
$x + 2 y = 3$
$2 y = - x + 3$
$y = - \frac{1}{2} x + \frac{3}{2}$

Y-intercept (plug in 0 for x):
$y = - \frac{1}{2} \left(0\right) + \frac{3}{2}$
$y = \frac{3}{2}$

X-intercept (plug in 0 for y):
$0 = - \frac{1}{2} x + \frac{3}{2}$
$- \frac{3}{2} = - \frac{1}{2} x$
$x = 3$

Jan 7, 2017

To find the $x$ intercept substitute $0$ for $y$ in the equation.

To find the $y$ intercept substitute $0$ for $x$ in the equation.

See the full explanation below

#### Explanation:

To find the $x$ intercept substitute $0$ for $y$ in the equation and solve for $x$.

$4 x + \left(8 \times 0\right) = 12$

$4 x + 0 = 12$

$4 x = 12$

$\frac{4 x}{\textcolor{red}{4}} = \frac{12}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} = 3$

$x = 3$

The x-intercept is $3$ or (3, 0)

To find the $y$ intercept substitute $0$ for $x$ in the equation and solve for $y$.

$\left(4 \times 0\right) + 8 y = 12$

$0 + 8 y = 12$

$8 y = 12$

$\frac{8 y}{\textcolor{red}{8}} = \frac{12}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} y}{\cancel{\textcolor{red}{8}}} = \frac{4 \times 3}{4 \times 2}$

$y = \frac{\cancel{4} \times 3}{\cancel{4} \times 2}$

$y = \frac{3}{2}$

The y-intercept is $\frac{3}{2}$ or (0, 3/2)