Question

What is the equation of the line that passes through the point (7,-6)and has a slope of -2

Answer 1

The equation of the required line is: 2x + y = 8

Explanation:

When a point on the line and the slope of the line are given, we use the slope - one - point form to determine the equation of the line.

Say,
`$ (x_1, y_1) $` is the point passing through the line and the slope of the line is say,
`m`. Then the equation would be:

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

Here
`$ (x_1, y_1) = (7, -6) $` and slope,
`$ m = - 2 $`.

Therefore, the equation of the line becomes:

`$ y - (-6) = -2(x - 7) $`

`$ \implies y + 6 = -2x + 14 $`

Rearranging we get:

`$ 2x + y - 8 = 0 $` which is the required equation of the line.