Question

Find the equation of a line intersecting the X-axis at a distance of 3 units to the left of the origin and of slope −2.

Answer 1

Given values:

If the line intersects the X-axis at a distance of 3 units to the left of the origin, then this corresponds to the point (−3, 0),

Point (x₁, y₁) = (−3, 0)

Slope (m) = −2

Using the point–slope formula:

y − y₁ = m(x − x₁)

Substitute x₁ = −3, y₁ = 0, and m = −2

y − 0 = −2[x − (−3)]

y = −2x − 6

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

∴ 2x + y + 6 = 0

Hence, the equation of a line is 2x + y + 6 = 0.