Question

Determine the equation of a line passing through the point (−1, −2) and having slope `4/7`.

Answer 1

Given values:

Point (x₁, y₁) = (−1, −2), Slope (m) = `4/7`

Using the point–slope formula:

y − y₁ = m(x − x₁)

y − (−2) = `4/7` . (x − (−1))

y + 2 = `4/7` (x + 1)

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

7(y + 2) = 4(x + 1)     ...[Multiplied both sides by 7 to remove the fraction]

7y + 14 = 4x + 4

0 = 4x − 7y + 4 − 14

∴ 4x − 7y − 10 = 0

Hence, the equation of a line is 4x − 7y − 10 = 0.