# What is the slope and intercept of -x-10y=20?

May 21, 2016

Slope: $\left(- \frac{1}{10}\right) \textcolor{w h i t e}{\text{XXXXX}}$y-intercept: $\left(- 2\right)$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} - x - 10 y = 20$

Convert this into the 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 $\textcolor{b l u e}{b}$

$- x - 10 y = 20$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow - 10 y = x + 20$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow y = \textcolor{g r e e n}{- \frac{1}{10}} x \textcolor{b l u e}{- 2}$

which is the slope-intercept form
with slope color(green)(""(-1/10)) and y-intercept color(blue)(""(-2))

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Typically it is only the y-intercept that is required in this type of question, but if the x-intercept is also desired:

Set $y = 0$ in the original equation (the x-intercept occurs on the X-axis where $y = 0$).

$\textcolor{w h i t e}{\text{XXX}} - x - 10 \left(0\right) = 20$

$\textcolor{w h i t e}{\text{XXX")rarr x=color(red)(} \left(- 20\right)}$

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Here is what the graph of this equation looks like:
graph{-x-10y=20 [-24.6, 3.86, -7.37, 6.87]}