# How do you find the x and y intercepts for y= -3x-9?

the x-intercept $= \left(- 3 , 0\right)$
the y-intercept $= \left(0 , - 9\right)$

#### Explanation:

To solve for the x-intercept, set $y = 0$ then solve for x

$y = - 3 x - 9$
$0 = - 3 x - 9$
$3 x = - 9$

$x = - 3$ when $y = 0$

therefore $\left(- 3 , 0\right)$ is the x-intercept

To solve for the y-intercept, set $x = 0$ then solve for y

$y = - 3 x - 9$
$y = - 3 \left(0\right) - 9$
$y = - 9$ when $x = 0$

therefore $\left(0 , - 9\right)$ is the y-intercept

God bless....I hope the explanation is useful.

Apr 23, 2016

${y}_{\text{intercept}} = - 9 \to \left(x , y\right) \to \left(0 , - 9\right)$

${x}_{\text{intercept}} = - 3 \to \left(x , y\right) \to \left(- 3 , 0\right)$

#### Explanation:

$\textcolor{b l u e}{{y}_{\text{intercept}} = - 9}$

The graph crosses the x-axis when y=0

Substituting $y = 0$ gives#

$0 = - 3 x - 9$

Add $\textcolor{b l u e}{9}$ to both sides

$\textcolor{b r o w n}{0 \textcolor{b l u e}{+ 9} = - 3 x - 9 \textcolor{b l u e}{+ 9}}$

$9 = - 3 x + 0$

Divide both sides by $\textcolor{b l u e}{3}$

$\textcolor{b r o w n}{\frac{9}{\textcolor{b l u e}{3}} = \frac{- 3}{\textcolor{b l u e}{3}} \times x}$

But $\frac{9}{3} = 3 \text{ and } \frac{- 3}{3} = - 1$

$\implies 3 = \left(- 1\right) \times x$

$- x = 3$

Multiply both sides by (-1)

$x = - 3$

$\textcolor{b l u e}{{x}_{\text{intercept}} = - 3}$
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