Question

What is the y intercept for a line with point (12,-7) slope 5/2?

Answer 1

y-intercept: `(-37)`

Explanation:

Step 1: Write equation in "point-slope form"
The point-slope form for a line with a slope of `m` through a point `(hatx,haty)` is
`color(white)("XXX")(y-haty) = m(x-hatx)`

For the given slope and point, this becomes
`color(white)("XXX")(y+7)=5/2(x-12)`

Step 2: Convert to "slope-intercept form"
The slope-intercept form for a line with slope `m` and y-intercept `b` is
`color(white)("XXX")y=mx+b`

Starting with
`color(white)("XXX")y+7 = 5/2(x-12)`

`color(white)("XXX")y+7 = 5/2x-30`

`color(white)("XXX")y=5/2x-37`
which is the "slope-intercept form with y-intercept -37#