Question

What is the y intercept for a line with point (3,-5) slope -4/3?

Answer 1

y-intercept: `(-1)`

Explanation:

"slope-point form" for a linear equation with slope `m` through the point `(hatx,haty)` is
`color(white)("XXX")y=m(x-hatx)+haty`
For the given values this becomes
`color(white)("XXX")y = (-4/3)(x-3)+(-5)`

Simplifying
`color(white)("XXX")y=-4/3x +4 -5`
or
`color(white)("XXX")y = -4/3x-1`
which is the "slope-intercept form"
with slope `= -4/3`
and
y-intercept `=-1`