# What are the intercepts of 3x+2y=12?

May 24, 2018

The x-intercept is $\left(4 , 0\right)$.
.
The y-intercept is $\left(0 , 6\right)$.

#### Explanation:

Given:

$3 x + 2 y = 12$

This is the formula for a linear equation in standard form. This is the easiest equation for finding the intercepts. To find the x- and y-intercepts, substitute $0$ for one variable, and solve for the other.

X-intercept: value of $x$ when $y = 0$

Substitute $0$ for $y$ and solve for $x$.

$3 x + 2 \left(0\right) = 12$

$3 x = 12$

Divide both sides by $3$.

$x = \frac{12}{3}$

$x = 4$

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

Y-intercept: value of $y$ when $x = 0$

Substitute $0$ for $x$ and solve for $y$.

$\left(0\right) + 2 y = 12$

$2 y = 12$

Divide both sides by $2$.

$y = \frac{12}{2}$

$y = 6$

The y-intercept is $\left(0 , 6\right)$.

graph{3x+2y=12 [-10.92, 11.58, -3.825, 7.425]}