Question

How do you write an equation in point slope form that passes through (-2,-8) and parallel to line whose equation is `y=-3x+2`?

Answer 1

`y=-3x+2` is a linear equation in slope-intercept form with
slope `m=(-3)`
(and y-intercept `=2`)

We want the equation of a line with slope `m=color(red)((-3))` through the point `(color(blue)(-2),color(green)(-8))`

Using the point-slope linear equation form:
`(y-color(blue)((-8))) = color(red)((-3))(x-color(green)((-2)))`

Simplifying
`y+8 = -3x-6`
or, in standard form
`3x+y = -14`