Question

Parallel and Perpendicular Lines? 15 Problems, 3 instructions. No problem if you can't help with them all. Questions will be posted below shortly...

Answer 1

"Write an equation of the line that passes through the given point and is parallel to the graph of the given equation."
#1. (3,2); y=3x-2
#2. (-4,-1); y=2x+14
#3. (-8,6); y=-1/4x+5
#4. (6,2); y=2/3x+19
#5. (10,-5); y=3/2x-7
#6. (-3,4); y=2

"Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain."
#7. y=4x+5
-4x+y=-13
#8. y=7/9x-7
y=-7/9x+3
#9. y=7/8
x=-4
#10. y=-6x-8
-x+6y=12
#11. 3x+6y=12
y-4=-1/2(x+2)
#12. y=4x+12
x+4y=32

"Determine whether each statement is always, sometimes, or never true. Explain."
#13. Two lines with different slopes are perpendicular.
#14. The slopes of vertical lines and horizontal lines are opposite reciprocals.
#15. A vertical line is perpendicular to the x-axis.

Answer 2

@erdog82

Answer 3

PLEASE SHOW WORK AND ANSWER! (:

Answer 4

Okay, to the first item, you need to know the way to build a line equation with the slope and a point. If you have your equation written like y=sx+c, then s is the slope, so for example en #1 (3,2); y=3x-2 , the slope of the line is 3, that means that you want to build another line, that must have the same slope (parallel lines have the same slope), so you'll use this equation

y-y1=s(x-x1),
where x1 and y1 are the coordinates of your point (in the case of question #1, x1=3 and y1=2

So, you'll get
y-2=3(x-3)
y=3x-7
The others of the first items are solved on the same way, but take a close eye on #6.

For the second item is pretty simple, if the slopes are the same, they're parallel, if by multiplying the slopes s1*s2=-1 then, they're perpendicular.
So, let's solve #7
y=4x+5
-4x+y=-13

The first slope is 4
For the second line, you must rearrange your equation, you'll habe y=4x-13 (Just add 4x in both sides), then the slope of the second line is 4
Now, both slopes are equal, that means these lines are parallel

For 13-15 ask the questions you have, but try doing 'em alone.

Answer 5

Ok. Im not working on it right nooow. I have to clean my room, but ill definitely try them in 15-20 mins. (:

Answer 6

Don't worry, i'll have to study my things for a while, feel free to ask. And if i'm not here, There're plenty of others.

Answer 7

ok hey

Answer 8

Lol I did #13-15 first. Heres what I got:
13. sometimes
14. sometimes (I had trouble with this one)
15. always

Answer 9

@zaynahf @Butterfly16

Answer 10

check out 14, the slopes of a vertical line are not defined and for an horizontal line are 0

Answer 11

so its never?

Answer 12

yup

Answer 13

ok

Answer 14

ok so #1. im so confused

Answer 15

okay, there's an (i don't know how to say it, i guess equation is fine) that defines the line that you form having a slope and a point. In other words, you are gonna build a new equation for a new line, having a point (that belongs to that line) and its slope.
Let's call s to the slope, x1 and y1 to the coordinates (x,y) of your point, so you'll have (x1,y1)
So, our new line is defined by
y-y1=s*(x-x1)

Answer 16

ok so now what?

Answer 17

When two lines are parallel, their slopes are the same, for example, if you graph y=x and y=x+1


Now, when your line equations are in the form y=sx+b, the slope is s, if you have 3y=6x-3, you'll have to transform it, so you start dividing by 3, and you'll get y=2x-1, then your slope is 2, got it?

Now, to build a parallel line you find the slope, and use the equation from the previopus answer with the point that the exercise has on it

Answer 18

ill try it a little. idk ill see...

Answer 19

Go ahead, trying on your own is one of the best ways to learn

Answer 20

thanks

Answer 21

#1. i got y=3x-4 ...

Answer 22

@Butterfly16 @zaynahf

Answer 23

Write your development...

Answer 24

Can you please try posting only one question per post? It helps the answerer focus on one thing at a time. Thanks!

Answer 25

#1.
(3,2); y=3x-2
y-y1=m(x-x1)
y-2=3(x-3)
y-2=3x-6
+2 +2
y=3x-4

Answer 26

3*-3=-9

Answer 27

#2.
(-4,-1); y=2x+14
y-y1=m(x-x1)
y+1=2(x+4)
-1 -1
y=2(x+3)
y=2x+6

Answer 28

In case #2 you have to expand the parenthesis first

Answer 29

I think I get it when the number is a fraction, but when it becomes a whole number I seem to get lost when computing the answer

Answer 30

You're right in the method, but you had problems with the arithmetic parts, aka the multiplications xd

Answer 31

Yeah. Math is my WEAKEST subject.

Answer 32

^^ Don't worry, is a process. When I had 12-13 i had bad grades, then 7/7 till i reach university xD

Answer 33

can you help with #6. its really confusing

Answer 34

Sure, in that case you obtain an horizontal line, that means that for any value of x, y=2
So, the parallel that has y=4 means that for every value of x, y=4, or in other words, your new line is y=4

Answer 35

idk. I'm going to bed. goodnight.

Answer 36

night