Question

Which of these equations is for a line perpendicular to y-3=5(x-2)?

Answer 1

Answer:

C

Step-by-step explanation:

y-3=5(x-2)  (rearrange this to be in slope- intercept from) (add 3 to both sides)

y = 5(x-2) + 3   (distribute parentheses)

y = x(5) - 2(5) + 3

y = 5x -10 + 3

y = 5x - 7

recall that for a line with gradient m, the gradient of the perpendicular line will be - (1/m)

hence in our case, our gradient of the original line is 5, hence the gradient of the perpendicular line is -1/5

From the choices, the only one that is consistent with this is C

i.e choice C:

5y + x = 25

5y = -x + 25

y = -(1/5) x + 5   ===> gradient of -1/5