Question

What is the relationship between the lines determined by the following two equations?

15x – 3y = –12
y = 5x + 7

A.
neither parallel nor perpendicular

B.
perpendicular

C.
parallel

D.
they are the same line

Answer 1

@TheSmartOne I think I have a feeling of how to do this so hang on

Answer 2

ok :)

Answer 3

Solve for y for the top equation

-3y = -15x -12
y= 5x-12

They have the same slope, so that should give you the answer

Answer 4

3y = -12 + 15x or 3y = 15x + -12

Then

y = 15/3x - 4 @TheSmartOne is this correct?

Answer 5

Then I would graph them.

Answer 6

hold on

Answer 7

it should be -3y for the first equation

Answer 8

and if you're going to graph them at the end, you might as well graph them from what you were already given :P

Answer 9

https://www.desmos.com/calculator/eswtpvk3cm

Answer 10

But you don't have to graph them, just looking at the slopes should give you the answer

Answer 11

Oh so would it be neither paralell or perpendicular?

Answer 12

Or the same line?

Answer 13

hold on @Abbster2015

Answer 14

First let's make this 15x – 3y = –12 into slope-intercept form

15x – 3y = –12

We can rearrange the terms so:

-3y + 15x = -12

subtract 15x on both sides :)

Answer 15

-3y = 15x +12

Answer 16

we need to subtract 15x, not add it :)

Answer 17

so try again :)

Answer 18

-3y = 15x - 12

Answer 19

If the slopes are the exact same, but they have different y-intercepts, then they are parallel

If the slopes are negative opposite reciprocals, then they are perpendicular

ex
7 and 7 would be parrllel, but 7 and (-1/7) would be perpendicular

Answer 20

still wrong :P

look at it this way

-3y + 15x = -12

Subtract 15x on both sides

-3y + 15x - 15x = -12 - 15x

-3y = -12 - 15x

And if you rearrange the terms

-3y = -15x - 12

Answer 21

now divide -3 on both sides :)

Answer 22

y = -15/3x - 4

Answer 23

@TheSmartOne

Answer 24

wrong and wrong :P

Answer 25

Dang it

Answer 26

we need to divide -3 on both sides

so what is -15/ -3 = ?

what is -12/ -3 = ?

since both numbers have negatives, we can cross it out :)

-15/-3 = 15/3 = ?

-12/-3 = 12/3 = ?

Answer 27

4

Answer 28

and what is 15/3 = ?

Answer 29

5

Answer 30

so the final equation is

y = 5x + 4

Answer 31

Oh okay so it would be Paralell?

Answer 32

and our second equation which was given to us was:
y = 5x + 7

so they both have the same slope of 5... what does that mean? Are they parallel, perpendicular, both, or none? :P

Answer 33

parallell?

Answer 34

correct :)

Answer 35

Yes! I am almost done now!