# What is the slope and intercept of -12x-4y=2?

May 18, 2016

Slope: $\left(- 3\right)$
y-intercept: $- \frac{1}{2}$

#### Explanation:

The easiest way to handle this question is to convert
the given equation: $- 12 x - 4 y = 2$
into "slope-intercept" form:
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} x + \textcolor{b l u e}{b}$ with slope $\textcolor{g r e e n}{m}$ and y-intercept $\textcolor{b l u e}{b}$

$- 12 x - 4 y = 2$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow - 4 y = 12 x + 2$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow y = \textcolor{g r e e n}{- 3} x \textcolor{b l u e}{- \frac{1}{2}}$
which is in slope-intercept form with slope color(green)(""(-3)) and y-intercept color(blue)(""(-1/2))

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If the x-intercept is also required,
it can be found by setting $y = 0$ in the original equation
and solving for $x$
$\textcolor{w h i t e}{\text{XXX}} - 12 x - 4 \left(0\right) = 2$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = - \frac{1}{6}$