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Question
The equation of a line is 3x + 4y – 7 = 0. Find:
- the slope of the line.
- 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)
4y = −3x + 7
`y = (-3)/4 x + 7/4`
i. Slope of the line = m = `(-3)/4`
ii. Slope of the line perpendicular to the given line = `(-1)/((-3)/4) = 4/3`
Solving the equations x − y + 2 = 0 and 3x + y − 10 = 0, we get x = 2 and y = 4.
So, the point of intersection of the two given lines is (2, 4).
Given that a line with slope `4/3` passes through point (2, 4).
Thus, the required equation of the line is
y − y1 = m(x − x1)
`y - 4 = 4/3 (x - 2)`
3(y − 4) = 4(x − 2)
3y − 12 = 4x − 8
4x − 3y + 4 = 0
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