# How do you find the x and y intercepts for -2x+3y=6?

May 17, 2016

Intercept on $x$ axis is $- 3$ and

intercept on $y$ axis is $2$.

#### Explanation:

For finding $x$ and $y$ intercepts of $- 2 x + 3 y = 6$

Let us first put $y = 0$ (to find intercepts on $x$ axis)

or $- 2 x + 0 = 6$ or $x = - 3$.

Hence, intercept on $x$ axis is $- 3$

For intercepts on $y$ axis, put $x = 0$ i.e.

$3 y = 6$ or $y = 2$

Hence, intercept on $y$ axis is $2$.

The other way is to convert equation in the form $\frac{x}{a} + \frac{y}{b} = 1$, where $a$ is intercept on $x$ axis and $b$ is intercept on $y$ axis.

As $- 2 x + 3 y = 6$, dividing by $6$ we get

$\frac{- 2 x}{6} + \frac{3 y}{6} = 1$ or $\frac{x}{- 3} + \frac{y}{2} = 1$

Hence, $- 3$ is intercept on $x$ axis and $2$ is intercept on $y$ axis.

graph{-2x+3y=6 [-10, 10, -5, 5]}