Question

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

Answer 1

Slope: `(-3)`
y-intercept: `-1/2`

Explanation:

The easiest way to handle this question is to convert
the given equation: `-12x-4y=2`
into "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)`

`-12x-4y=2`
`color(white)("XXX")rarr -4y=12x+2`

`color(white)("XXX")rarr y=color(green)(-3)xcolor(blue)(-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`
`color(white)("XXX")-12x-4(0)=2`

`color(white)("XXX")rarr x=-1/6`