Question

Write an equation of the line that passes through the points 0, -1 and 2,3

Answer 1

`$ 2x - 2y - 1 = 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) = (0, -1) $` and
`$ (x_2, y_2) = (2, 3)$`

Therefore we have:
`$ (y + 1)/(3 + 1) = (x - 0)/(2 - 0) $`

`$ \implies (y + 1)/(4) = (x)/(2) $`

`$ \implies 2y + 2 = 4x\\ = 4x - 2y - 2 = 0  $`

Multiplying by
`$ (1)/(2) $` through out we get:
`$ 2x - 2y - 1 = 0$`.