# What are the x and y intercepts of the linear equation: -y=(3x+6)-12?

May 19, 2018

y-int = 6
x-int = 2

#### Explanation:

$- y = \left(3 x + 6\right) - 12$

first remove the parentheses:
$- y = 3 x + 6 - 12$

combine like terms
$- y = 3 x - 6$

multiply both sides by -1
$\left(- 1\right) - y = \left(- 1\right) \left(3 x - 6\right)$

$y = - 3 x + 6$

to find the y-intercept set x = 0

$y = - 3 \left(0\right) + 6$

$y = 6$

to find the x-intercept set y = 0

$0 = - 3 x + 6$

$- 6 = - 3 x$

$2 = x$ or $x = 2$

graph{y=-3x+6 [-13.71, 14.77, -6.72, 7.52]}

May 19, 2018

$x -$intercept is $\left(2 , 0\right)$
$y -$intercept is $\left(0 , 6\right)$

#### Explanation:

$- y = \left(3 x + 6\right) - 12$

First let's restate the equation in more common form.

(i) The parentheses are serving on purpose here.

$- y = 3 x + 6 - 12$

$- y = 3 x - 6$

(ii) Multiply through by $- 1$

$y = - 3 x + 6$

Here we have the equation in slope/intercept form: $y = m x + c$

Hence the $y -$intercept is $\left(0 , 6\right)$

The $x -$intercept occurs where $y = 0 \to$

$0 = - 3 x + 6$

$3 x = 6 \to x = 2$

$\therefore$ the $x -$intercept is $\left(2 , 0\right)$

These intercepts can be seen on the graph of $y$ below.

graph{-y =(3x+6)-12 [-16.03, 16.01, -8, 8.03]}