# How do you find x and y intercepts of  -6x + 3y = -9?

Dec 17, 2016

#### Answer:

x-intercept is $x = \frac{3}{2}$ or (3/2, 0).

y-intercept is $y = - 3$ or (0, -3)

#### Explanation:

To find the x-intercept, set $y$ equal to $0$ and solve for $x$:

$- 6 x + 3 \cdot 0 = - 9$

$- 6 x + 0 = - 9$

$- 6 x = - 9$

$\frac{- 6 x}{-} 6 = \frac{- 9}{-} 6$

$\frac{\cancel{- 6} x}{\cancel{- 6}} = \frac{3}{3} \cdot \frac{- 3}{-} 2$

$x = 1 \cdot \frac{3}{2}$

$x = \frac{3}{2}$ or (3/2, 0).

To find the y-intercept, set $x$ equal to $0$ and solve for $y$:

$- 6 \cdot 0 + 3 y = - 9$

$0 + 3 y = - 9$

$3 y = - 9$

$\frac{3 y}{3} = \frac{- 9}{3}$

$\frac{\cancel{3} y}{\cancel{3}} = - 3$

$y = - 3$ or (0, -3)