Question

Find the equations of the line passing through the points (−1, 1) and (2, −4).

Answer 1

Given values:

Point A(x₁, y₁) = (−1, 1),

Point B(x₂, y₂) = (2, −4),

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

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

`m = (-4 - 1)/(2 - (-1))`

`m = (-5)/(2 + 1)`

∴ `m = -5/3`

Using the point–slope formula:

y − y₁ = m(x − x₁)

Substitute x₁ = −1, y₁ = 1, and m = `-5/3`

`y - 1 = - 5/3 [x - (-1)]`

3(y − 1) = −5(x + 1)   ...[Multiplied both sides by 3 to eliminate the fraction.]

3y − 3 = −5x − 5

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

5x + 3y − 3 + 5 = 0

∴ 5x + 3y + 2 = 0

Hence, the equation of the line is 5x + 3y + 2 = 0.