The equation of a line is 3x + 4y – 7 = 0. Find :

(i) the slope of the line

(ii) 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.

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Solution

3x + 4y - 7 = 0 ...(1)

4y = -3x + 7

y = $fraction numerator negative 3 over denominator 4 end fraction x plus 7 over 4$

(i) Slope of the line = m = $fraction numerator negative 3 over denominator 4 end fraction$

(ii) Slope of the line perpendicular to the given line = $fraction numerator negative 1 over denominator begin display style fraction numerator negative 3 over denominator 4 end fraction end style end fraction equals 4 over 3$

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 passes through point (2, 4).

Thus, the required equation of the line is

y - 4 = (x - 2)

3y - 12 = 4x - 8

4x - 3y + 4 = 0

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