# What are the intercepts of 3y-2x=5?

Dec 20, 2015

y-intercept: $\frac{5}{3}$
x-intercept: $\left(- \frac{5}{2}\right)$

#### Explanation:

The y-intercept is the value on the Y-axis where the equation crosses the Y-axis. Since for all point on the Y-axis, $x = 0$, another way to say this is that the y-intercept is the value of $y$ when $x = 0$

Given: $3 y - 2 x = 5$
when $x = 0$
$\textcolor{w h i t e}{\text{XXX}} 3 y - 2 \times 0 = 5 \Rightarrow y = \frac{5}{3}$
So the y-intercept is $\frac{5}{3}$

Similarly the x-intercept is the value of $x$ when $y = 0$
$\textcolor{w h i t e}{\text{XXX}} 3 \times 0 - 2 x = 5 \Rightarrow x = - \frac{5}{2}$
So the x-intercept is $\left(- \frac{5}{2}\right)$