Question

Find the equations of the line passing through the points (−1, −2) and (2, 1).

Answer 1

Given values:

Point A(x₁, y₁) = (−1, −2),

Point B(x₂, y₂) = (2, 1),

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂):

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (1 - (-2))/(2 - (-1))`

`m = (1 + 2)/(2 + 1)`

`m = 3/3`

∴ m = 1

Using the point–slope formula:

y − y₁ = m(x − x₁)

Substitute x₁ = −1, y₁ = −2, and m = 1

y − (−2) = 1[x − (−1)]

y + 2 = x + 1

Let’s write the above equation in standard form (Ax + By + C = 0),

x − y + 1 − 2 = 0

∴ x − y − 1 = 0

Hence, the equation of the line is x − y − 1 = 0.