Question

Answer the following question:

Find the X−intercept of the line whose slope is 3 and which makes intercept 4 on the Y−axis

Answer 1

Equation of a line having slope ‘m’ and y-intercept ‘c’ is y = mx + c

Given, m = 3, c = 4

∴ The equation of the line is

y = 3x + 4

∴ 3x – y = – 4

∴ `(3x)/((-4)) - y/((-4))` = 1

∴ `x/(((-4)/3)) + y/4` = 1

This equation is of the form `x/"a" + y/"b"` = 1, where x-intercept = a

∴ x-intercept = `(-4)/3`

Alternate Method:

Let θ be the inclination of the line.

Then tan θ = 3    ...[∵ slope = 3 (given)]

∴ `"OB"/"OA"` = 3

∴ `4/"OA"` = 3

∴ OA = `4/3`

∴ x-intercept = `-4/3` as point A is to the left side of Y-axis.