Question: Which of the following lines is perpendicular to the line passing through the points (6, 7) and (8, - 9)?

A ) y = - 8x + 19
B ) y = 1 / 8x + 6
C ) y = - 1 / 8x - 7 / 8
D ) y = 8x - 17

Steps to derive

7 Slope of the line passing through the points (x₁, y₁) and (x₂, y₂) is y2-y1x2-x1.

8 Slope of the line passing through the points (6, 7) and (8, - 9) is - 9 - 78-6 = - 8.

9 If m is the slope of the line perpendicular to the line passing through the points (6, 7) and (8, - 9), then
m × - 8 = - 1 ⇒ m = 1 / 8

10 

Equation	Slope
y = 1 / 8x + 6 y = - 8x + 19 y = - 1 / 8x - 7 / 8 y = 8x - 17	1 / 8 - 8 - 1 / 8 8

 [Find the slope of the line using y = mx + b.]

11 So, the line y = 1 / 8x + 6 is perpendicular to the line passing through the points (6, 7) and (8, - 9).



Hence the right answer is Option B

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