Question

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Answer 1

3x + 4y - 7 = 0 (given)

Rearrange the equation to the format: y = mx + c

3x + 4y - 7 = 0

4y = -3x + 7

y = -3/4 x + 7/4

Identify the slope, which is m in the equation y = mx + c

y = -3/4 x + 7/4

Slope = m = -3/4

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Find the slope of the perpendicular line

Slope = negative reciprocal of the perpendicular line

Slope = 4/3

Find the intersection point:

x - y + 2 = 0 ------------ [ 1 ]

3x+ y - 10 = 0  ------------ [ 2 ]

Add [ 1 ] and [ 2 ]:

4x - 8 = 0

4x = 8

x = 2 ------------ Sub into equation [ 1 ] to find y

x - y + 2 = 0

2 - y + 2 = 0

4 - y = 0

y = -4

The intersection point is (2, -4)

Find the y-intercept of that perpendicular line:

y = mx + c

y = 4/3 x + c

At ( 2, -4)

-4 = 4/3 (2) + c

c = -4 - 8/3

c = -20/3

Find the equation:

y = mx + c

y = 4/3 x - 20/3

3y = 4x - 20

Answer: (i) The slope is - 3/4 (ii) The equation is 3y = 4x - 20