# How do you find the x and y intercept of 3x − 5y = −10?

Apr 8, 2017

Isolate for each variable by subbing in $0$ for the other. In this case, we get $\left(- \frac{10}{3} , 0\right)$ as the $x$-intercept, and $\left(0 , 2\right)$ as the $y$-intercept.

#### Explanation:

To find the zeros, all we have to do is sub in one variable as $0$ and isolate for the other.

Solving for $x$-intercept

This happens when the $y$-value is $0$, thus we sub in $0$ as the $y$-value.

$3 x - 5 y = - 10$

$3 x - 5 \left(0\right) = - 10$

Now we solve for $x$.

$3 x - 0 = - 10$

$3 x = - 10$

$x = - \frac{10}{3}$

The $x$-intercept is $\left(- \frac{10}{3} , 0\right)$.

Solving for $y$-intercept

This happens when the $x$-value is $0$, thus we sub in $0$ as the $x$-value.

$3 x - 5 y = - 10$

$3 \left(0\right) - 5 y = - 10$

Now we solve for $y$.

$- 5 y = - 10$

$y = \frac{- 10}{-} 5$

$y = 2$

The $y$-intercept is $\left(0 , 2\right)$.

We can graph the equation to check our work.

graph{3x - 5y = -10 [-10, 10, -5, 5]}

As we can see, our intercepts are correct.

Hope this helps :)