Question

Find the equations of the line passing through the points (2, 3) and (5, −2).

Answer 1

Given values:

Point A(x₁, y₁) = (2, 3),

Point B(x₂, y₂) = (5, −2),

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

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

`m = (-2 - 3)/(5 - 2)`

∴ `m = (-5)/(3)`

Using the point–slope formula:

y − y₁ = m(x − x₁)

Substitute x₁ = 2, y₁ = 3, and m = `-5/3`,

`y - 3 = - 5/3 (x - 2)`

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

3(y − 3) = −5(x − 2)     ...[Multiplied both sides by 3 to eliminate the fraction.]

3y − 9 = −5x + 10

5x + 3y − 9 − 10 = 0

∴ 5x + 3y − 19 = 0

Hence, the equation of the line is 5x + 3y − 19 = 0.