Question

A line intersects x-axis at point (−2, 0) and cuts off an intercept of 3 units from the positive side of y-axis. Find the equation of the line.

Answer 1

Let line intersects x-axis at P(−2, 0) and cuts off an intercept of 3 units at Q.

∴ Co-ordinates of Q are (0, 3)

Now, slope of line PQ

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

= `(0 - 3)/(-2 - 0)`

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

= `3/2`

∴ Equation of line PQ will be

y − y₁ = m(x − x₁)

`=> y - 3 = 3/2 (x - 0)`

`=> y - 3 = 3/2 x`

`=>` 2y – 6 = 3x

`=>` 2y = 3x + 6

Hence, required equation of line is 2y = 3x + 6