# How do you find the x and y intercepts of 3x+4y=12?

Sep 26, 2016

x and y intercepts of $3 x + 4 y = 12$ is 4 and 3

#### Explanation:

subtitute $y = 0$ to find x intercepts

when $y = 0$

$3 x = 12$
$x = 4$

x intercepts is 4

subtitute $x = 0$ to find y intercepts

when $x = 0$

$4 y = 12$
$y = 3$

y intercepts is 3

Sep 26, 2016

x-intercept: $4$
y-intercept: $3$

#### Explanation:

The x-intercept is the value of $x$ when $y = 0$ (noting that $y = 0$ is the definition of the X-axis.
$\textcolor{w h i t e}{\text{XXX}} 3 x + 3 \textcolor{red}{y} = 12$ when $\textcolor{red}{y} = \textcolor{red}{0}$

$\textcolor{w h i t e}{\text{XXX}} 3 x + 4 \cdot \textcolor{red}{0} = 12$

$\textcolor{w h i t e}{\text{XXX}} x = 4$

Similarly, the y-intercept is the value of $y$ when $x = 0$ (definition of the Y-axis).
$\textcolor{w h i t e}{\text{XXX}} 3 \textcolor{b l u e}{x} + 4 y = 12$ when $\textcolor{b l u e}{x} = \textcolor{b l u e}{0}$

$\textcolor{w h i t e}{\text{XXX}} 3 \cdot \textcolor{b l u e}{0} + 4 y = 12$

$\textcolor{w h i t e}{\text{XXX}} y = 3$