Question

What is the equation in point slope form for the line that passes through the points (-1,3) and (-2,-3)

Answer 1

`$ 6x - y + 9 = 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) = (-1 , 3) $` and
`$ (x_2, y_2) = (-2, -3)$`.

Therefore we have:
`$ (y - 3)/(-3 - 3) = (x + 1)/(-2 + 1) $`

`$ \implies (y - 3)/(-6) = (x + 1)/(-1) $`

`$ \implies -y + 3 = -6x - 6   $`

Therefore, we have:
`$ 6x - y + 9 = 0 $`