Question

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

Answer 1

Slope: `(-1/10)color(white)("XXXXX")`y-intercept: `(-2)`

Explanation:

Given
`color(white)("XXX")-x-10y=20`

Convert this into the slope-intercept form
`color(white)("XXX")y=color(green)(m)x+color(blue)(b)`
with slope `color(green)(m)` and y-intercept `color(blue)(b)`

`-x-10y=20`
`color(white)("XXX")rarr -10y=x+20`

`color(white)("XXX")rarr y= color(green)(-1/10)xcolor(blue)(-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`).

`color(white)("XXX")-x-10(0)=20`

`color(white)("XXX")rarr x=color(red)(""(-20))`

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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]}