Question

What is the slope and y-intercept of the line 2x - 3y = -18?

Answer 1

slope `=2/3`
and\y-intercept `= 6`

Explanation:

Slope
For an equation in the form:
`color(white)("XXXX")` `Ax+By=C`
the slope is
`color(white)("XXXX")` `m = -A/B`
for the given equation `2x-3x=-12` this becomes
`color(white)("XXXX")` `m = 2/3`

Alternatively we could rewrite the given equation `2x-3y =-18`
into "slope intercept" form:
`color(white)("XXXX")` `y = mx+b`
`color(white)("XXXX")` `color(white)("XXXX")` `color(white)("XXXX")`where `m` is the slope and `b` is the y-intercept
`color(white)("XXXX")`2x-3y = -18#

`rarr` `color(white)("XXXX")` `-3y = -2x-18`

`rarr` `color(white)("XXXX")` `y = 2/3x +6`

y-intercept
If you rewrote the equation in "slope intercept form" (see above)
the slope can be read directly from the equation as
`color(white)("XXXX")` `m = 6`

Otherwise
note that the y-intercept is the value of `y` when `x=0` in the equation:
`color(white)("XXXX")` `2(0)-3y = -18`
`rarr` `color(white)("XXXX")` `y = 6`