Question

Find the equation of the line perpendicular to x–6y+7 =0 and passing through (3,–10)

Answer 1

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Answer 2

Find the gradient of the line  x– 6y + 7 = 0:

x– 6y + 7 = 0

6y = x + 7

y =  x/6  + 7/6

⇒  gradient is 1/6

Find the gradient of its perpendicular line:

The gradient of the perpendicular is its negative reciprocal

⇒ gradient = -6

Find the y-intercept:

Given that the line passed through (3, -10)

y = -6x + c

-10 = -6 (3) + c

-10 = -18 + c

c = 8

⇒ y-intercept = 8

Find the equation:

y = mx + c

y = -6x + 8

Answer: y = -6x + 8