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Question
The equation of a line 3x + 4y − 7 = 0. Find
1) The slope of the line.
2) The equation of a line perpendicular to the given line and passing through the intersection of the lines x – y + 2 = 0 and 3x + y – 10 = 0.
Solution
3x + 4y – 7 = 0 .....(1)
1) Slope of the line m = `"coefficient of x"/"coefficient of y" = -3/4`
2) Equation of line perpendicular to the given line
4x – 3y = λ ......(2)
Solving the equations x – y + 2 = 0 and 3x + y – 10 = 0, point of intersection is (2, 4).
Line (2) passes through points (2, 4).
4(2) – 3(4) = λ ⇒ λ = –4
Hence, the equation of required line is
4x - 3y + 4 = 0
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