Question

Consider the line y=8x-6 .

Find the equation of the line that is perpendicular to this line and passes through the point (-6,6) .

Find the equation of the line that is parallel to this line and passes through the point (-6,6) .

Answer 1

first we need to know the slope of y = 8x - 6.
Do you know the slope ?

Answer 2

In y = mx + b form, the slope is in the m position. So what number is in the m position ?

Answer 3

let me know when your ready to participate

Answer 4

8 is in the m place so its 8/1 , Rise over run . (:

Answer 5

correct....8 is the slope
A parallel line will have the same slope and a perpendicular line will have the negative reciprocal slope.

perpendicular line to y = 8x - 6....slope is 8. So we need negative reciprocal of 8. All that means is " flip " the slope and change the sign. So the negative reciprocal of 8 is -1/8. You see how I flipped the slope and changed the sign.

now we use y = mx + b and solve for b
y = mx + b
(-6,6) x = -6 and y = 6
slope(m) = -1/8
mow we sub
6 = -1/8(-6) + b
6 = 6/8 + b
6 - 6/8 = b
48/8 - 6/8 = b
42/8 = b (reduces to 21/4
so your perpendicular equation is : y = -1/8x + 21/4

any questions so far ?

Answer 6

Now for a parallel line, we use the same slope, which is 8

y = mx + b
(-6,6) x = -6 and y = 6
slope(m) = 8
now we sub
6 = 8(-6) + b
6 = - 48 + b
6 + 48 = b
54 = b
so your parallel equation will be : y = 8x + 54

Answer 7

Well that makes sense, Thank you for the step by step procedure. I really appreciate that! Ha, So the parallel is Y=8x+54 and perpendicular is Y=-1/8x+21/4 ?

Answer 8

do u need help or has @texaschic101 explained well enough @gabriel72alv ?

Answer 9

I think he explained it far enough as I needed, Thank you though @sayakdbz ! (:

Answer 10

parallel is y = 8x + 54 and perpendicular is y = -1/8x + 21/4
Glad I could help :)

Answer 11

do you have any questions at all ?