# What are the intercepts of 3x+9y=-12?

Feb 25, 2016

x-intercept: $\left(- 4\right)$
y-intercept: $\left(- \frac{4}{3}\right)$

#### Explanation:

Th x-intercept is the point where a graph of the line crosses the X-axis; since all points on the X-axis (and only those points) $y = 0$,
another way of saying this is that the x-intercept is the value of $x$ when $y = 0$
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{3 x + 9 \times 0 = - 12} \rightarrow \textcolor{b l u e}{3 x = - 12} \rightarrow \textcolor{g r e e n}{x = - 4}$

Similarly the y-intercept is the value of $y$ when $x = 0$
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{3 \times 0 + 9 y = - 12} \rightarrow \textcolor{b l u e}{9 y = - 12} \rightarrow \textcolor{g r e e n}{y = - \frac{4}{3}}$