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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
Solution
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.
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