Question

What is an equation of the line that passes through the points (4, -1)(4,−1) and (8, 5)(8,5)? Put your answer in fully reduced form.

Answer 1

`3x - 2y - 10 = 0 $`

Explanation:

When we are to find the equation of the line passing through two points, say
`$ (x_1, y_1) $` and
`$ (x_2, y_2) $` we use two -point form.

The two point form is as follows:

`$ (y - y_1)/(y_2 - y_1) = (x - x_1)/(x_2 - x_1) $`

Here
`$ (x_1 , y_1) = (4, -1) $` and
`$ (x_2 , y_2) = (8, 5) $`.

Therefore we have:
`$ (y + 1)/(6) = (x - 4)/(4) $`

`$ \implies 2y + 2 = 3x - 12 $`

Simplifying we get:
`$ 3x - 2y - 10 =0 $`.