Question

What is the equation of the line that passes through the point (3,-7) and has a slope of -4/3?

Answer 1

4x + 3y + 9 = 0

Explanation:

When a slope of a line and a point passing through it is given then we use slope - one point form to determine the equation of the line.

It is given by:

`$ (y - y_1) = m (x - x_1) $`

where
`$m$` is the slope of the line and

`$ (x_1, y_1) $` is the point passing through it.

Here,
`$ m = (-4)/(3) $` and
`$ (x_1 , y_1) = (3 , -7) $`.

Substituting in the formula
`y +  7 = (-4)/(3) (x - 3)`

`$ \implies 3y + 21 = -4x + 12 $`

`$ 4x + 3y + 9 = 0 $`