# What are the intercepts of 2x-3y=-7?

Apr 5, 2016

x-intercept: $- \frac{7}{2} = - 3 \frac{1}{2}$

y-intercept: $\frac{7}{3} = 2 \frac{1}{3}$

#### Explanation:

The x-intercept is the value of $\textcolor{b l u e}{x}$ when $\textcolor{red}{y = 0}$
$\textcolor{w h i t e}{\text{XXX}} 2 \textcolor{b l u e}{x} - 3 \left(\textcolor{red}{0}\right) = - 7$

$\textcolor{w h i t e}{\text{XXX}} 2 \textcolor{b l u e}{x} = - 7$

$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{x} = - \frac{7}{2}$

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The y-intercept is the value of $\textcolor{red}{y}$ when $\textcolor{b l u e}{x = 0}$
$\textcolor{w h i t e}{\text{XXX}} 2 \left(\textcolor{b l u e}{0}\right) - 3 \left(\textcolor{red}{y}\right) = - 7$

$\textcolor{w h i t e}{\text{XXX}} - 3 \left(\textcolor{red}{y}\right) = - 7$

$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{y} = \frac{7}{3}$