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Question
Find the equation of a line that has Y-intercept 3 units and is perpendicular to the line joining (2, – 3) and (4, 2).
Solution
Let m be the slope of required line
Slope of the given line = `(2 + 3)/(4 - 2) = (5)/(2)`.
But the required line is perpendicular to the given line.
Hence,
m x Slope of the given line = -1
⇒ m x `(5)/(2)` = -1
⇒ m = `(-2)/(5)`
Y-intercept, c = 3
Hence, equation of the required line is given by
y = mx + c
i.e., y = `-(2)/(5) x + 3`
⇒ 5y = -2x + 15
⇒ 2x + 5y - 15 = 0.
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