Question

Which of the following is the equation of a line perpendicular to the line y = -10x + 1, passing through the point (5,7)?

Answer 1

What are the options?

Answer 2

Perpendicular slope means it is the negative reciprocal of the original:
\[\LARGE m=-\frac{1}{m}\]

Answer 3

A.-1/10x+y=-13?2 B. 1/10x-y=-13/2 C.1/10x+4=-13?2 D. -1/10x-4=-13/2

Answer 4

first you need to find the slope of the line given. Do you know how to do that ?

Answer 5

no

Answer 6

a line in y = mx + b form, and the slope is in the m position.
y = -10x + 1. Can you tell what the slope is ?

Answer 7

yeah it -10

Answer 8

correct. Now we are looking for a perpendicular line, so we will need the negative reciprocal of that slope. All that means is " flip " the slope over and change the sign. For example, the negative reciprocal of slope -2 = 1/2. (see how I flipped the slope and changed the sign.) So, can you tell me what the negative reciprocal of slope -10 is ?

Answer 9

1/10???

Answer 10

correct. That is the slope we need.
Now, there are two ways to solve this.....we can either use y = mx + b form, and just solve for b, or we can use point slope form, which would you rather use ?

Answer 11

y=mx+b

Answer 12

let me show you....
y = mx + b
slope(m) = 1/10
(5,7) x = 5 and y = 7
now we sub and solve for b
y = mx + b
7 = 5(1/10) + b
7 = 5/10 + b
7 = 1/2 + b
7 - 1/2 = b
14/2 - 1/2 = b
13/2 = b
therefore, the perpendicular line we need is : y = 1/10x + 13/2 or in standard form :
-1/10x + y = 13/2 (multiply the equation by -1)
1/10x - y = -13/2 <-- your answer

do you have any questions ?

Answer 13

no thanks

Answer 14

I tried to explain the best I could...I hope you understand everything :)

Answer 15

yes thank you for everything