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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.
Solution
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
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