Question

What is the equation of the line through point (2, -3) with slope -4?

Answer 1

`4x+y=5`

Explanation:

The general slope-point for a line with slope `m` through a point `(hatx,haty)` is
`color(white)("XXX")(y-haty)=m(x-hatx)`

Given
`color(white)("XXX")m=(-4)`
`color(white)("XXX")(hatx,haty) = (2,-3)`
the slope-point form of the line is
`color(white)("XXX")(y+3)= (-4)(x-2)`

Converting to standard form:
`color(white)("XXX")y+3 = -4x+8`

`color(white)("XXX")4x+y=5`