Question

How do you write an equation in point slope form that passes through (0, -4) with slope -7?

Answer 1

In point slope form, the equation of the line is

`y - (-4) = -7(x - 0)`

This is of the form `y - y_0 = m(x - x_0)` where `m` is the slope and `(x_0, y_0)` is a point through which the line passes.

If we are less strict about it, this is written more cleanly as:

`y+4=-7x`

Answer 2

Given a point `(x_1,y_1)` and a slope of `m`
the point-slope form of its linear equation is
`y - y_1 = m(x - x_1)`

Given the point `(x_1,y_1)=(0,-4)` and the slope `m=(-7)`
this becomes
`y -(-4) = (-7)(x-0)`

This, of course, could be simplified; perhaps as
`y+4 = -7x`
but this loses some of the explicit information in the original form.