Question

How do you write an equation of a line with slope 2/3 and point is (8, -4)?

Answer 1

`2x-3y=28`

Explanation:

Given a slope of `color(green)m` through a point `(color(red)a,color(blue)b)`
the slope-point form of the line is
`color(white)("XXX")y-color(blue)b=color(green)m(x-color(red)a)`

For the given values this becomes
`color(white)("XXX")y-color(blue)(""(-4))=color(green)(2/3)(x-color(red)8)`

Simplifying
`color(white)("XXX")3y+12=2x-16`

or, in standard form
`color(white)("XXX")2x-3y=28`

or, you might want this in slope-intercept form:
`color(white)("XXX")y=2/3x-28/3`