Question

Write an equation of a line in slope intercept form that is parallel to y = 3x+6 and passes through the point (-10, 2.5)

and

Write an equation of a line in slope intercept form that is perpendicular to y = -4x -2 and passes through the point (-16, -11).

I just need someone to show me how to do perp. and parallel!

Answer 1

@Hero @JakeV8 Help please?

Answer 2

What is the slope of the first line... the line parallel to y = 3x + 6 ?

Answer 3

Well, the slope would still be 3 right?

Answer 4

right :)

But it's through a different point... so you need to write an equation where m = 3 but through point (-10, 2.5)

Use point-slope form: y - y1 = m(x - x1) where (x1, y1) = (-10, 2.5)

Answer 5

y-2.5=3(x+10) correct?

Answer 6

yes, very nice :)

Now simplify to make it more like y = mx + b in form...

Answer 7

y=3x+? I don't exactly get what the B would represent?

Answer 8

you had y - 2.5 = 3(x + 10) but you need it to be in slope intercept form, y = mx + b

notice there is no parenthesis in the y = mx + b form... you need to multiply out that parenthesis "3(x+10)".

Then you can move the 2.5 from the left side of the equation to the right side... then simplify the last time.

Give it a try... :)

Answer 9

Multipling "3(x+10)" would be 3x+30 but then how would I move the 2.5?

Answer 10

algebra ;)

y - 2.5 = 3x + 30

Add 2.5 to both sides...

y - 2.5 + 2.5 = 3x + 30 + 2.5
y = 3x + 30 + 2.5
y = 3x + 32.5

Answer 11

You may want to double check... make sure that equation goes through (-10, 2.5) by substituting those x and y in...

y = 3x + 32.5
2.5 = 3(-10) + 32.5
2.5 = -30 + 32.5
2.5 = 2.5 <<<<<<<------------ yay! we got it right!

Answer 12

So, y=3x+32.5 would be my answer right? If it is then I understand completely! Would I do the same for the perpindicular problems?

Answer 13

Yes, you got it. Quick review before perpendicular...

Parallel. Find a line parallel to some other line running through a point. First, slope is the same. Next, write point-slope form of line like y-y1 = m(x-x1), and plug in your slope and (x1,y1) point. Then multiply everything out and get the y all alone on the left side to end with the slope-intercept form of y = mx + b.

Answer 14

But yes, you understand, I think :)

So... perpendicular is ALMOST the same...
Write an equation of a line in slope intercept form that is perpendicular to y = -4x -2 and passes through the point (-16, -11).

What is the slope of the actual line, y = -4x -2 ?

What is the slope of the perpendicular line?

Answer 15

The actual line slope is -4. So would the perp. line slope be the opposite? so 4?

Answer 16

close, but not quite.

Slope of a perpendicular line is the "negative inverse"... you can think of it as opposite, in a way, but it's not just changing from negative to positive.

If slope is 3, then perpendicular slope is -(1/3)... it's the negative AND also you flip it upside down as a fraction.

So the slope perpendicular to 1/4 is -4...
the slope perp. to -4/7 is 7/4
and so on.

Answer 17

Does that make sense? You had the negative part correct, but you needed to also flip it over (i.e. "take the inverse")

Answer 18

So, it would be 1/4!! so y=1/4x+b, we've got that so far! Then what?

Answer 19

wait... hold on a sec :)

Yes, so the slope of the perpendicular line is (1/4). And remember, it has to run through that point (-16, -11) that was given in part 2 of the problem.

So now it's the same process as you used for parallel... write it as point-slope form and then simplify to get slope intercept form with y = mx + b

Answer 20

Okay! point-slope form would be y+11=1/4(x+16)
then 1/4x+64
y+11=1/4x+64
y+11-11=1/4x+64-11
y=1/4x+55?

Answer 21

So close... very close. If you weren't online, you would want to check that equation and see if it did actually go through (-16,-11)

so (-11) = (1/4)(-16) + 55
-11 = -4 + 55
-11 = 51 <<<<<<<<<<------- AACK! Not correct!!!

You didn't multiply out the parenthesis correctly in your first step...

y + 11 = 1/4(x + 16)

you need to remember to multiply that "1/4" across both the "x" and the 16...
y + 11 = 1/4 x + (1/4)(16)
y + 11 = 1/4 x + 4

Answer 22

OHHH! Yes, I completely forgot to simplify that! So then,
y+11-11=1/4x+4-11
y=1/4x-7?

Answer 23

yay! You got it... but you still might want to double check:

y = 1/4 x - 7
and it runs through (-16,-11)
so:
-11 = (1/4)(-16) - 7
-11 = -4 - 7
-11 = -11 <<<-------- Yay! You got it right!

Answer 24

Finally! I understand! Thank you so much!

Answer 25

So, to review... parallel has same slope, perpendicular has negative inverse slope.

To find an equation of a line through a point when you know the slope, write it in "point slope form" (cool name, since it makes sense!!). Then simplify to make it like point intercept form, y = mx + b

Answer 26

Extra bonus points for your persistence trying to learn this... it's always nice to help someone who is willing to try to solve the problems rather than wait for the answers :)

Keep it up :)

Answer 27

I have done every single problem right but there is this last one that is set up weird?

Write an equation of a line in slope intercept form that is perpendicular to the line 2x -3y = 12 and passes through the point (2, 6).

Answer 28

So, you've seen two forms of line equations... slope intercept like y = mx + b and point slope, like y - y1 = m(x - x1)

The third form of a line equation is called the "standard form" and it looks like:
Ax + By = C
so that's the form they are giving you here... A would be 2, B would be -3, and C would be 12. By the way, this is my least favorite :)

But again, you need to try to solve for slope so you can find the perpendicular line.

So, you need to use algebra to modify 2x - 3y = 12 to a form like y = mx + b where you know the slope is "m"

Answer 29

When you do that algebra, you want to solve for "y" on the left side...

2x - 3y = 12 <<--- start by subtracting 2x from both sides...

Answer 30

2x-2x+3y=12-2x
3y=12-2x but how do I take away 2x if there are no x's?

Answer 31

you accidentally switched the -3y to be just 3y in the first line...

Let's start it again:
2x - 3y = 12 <<--- start by subtracting 2x from both sides...
2x -2x - 3y = 12 - 2x
-3y = 12 - 2x
Now you need to divide both sides by -3 to solve for y:
-3y/(-3) = (12-2x)/(-3)
y = (12 - 2x) / (-3)

But you need to simplify that right side down to get rid of the parenthesis... so divide both the 12 and the -2x by -3

Answer 32

You asked about taking away 2x from no x's...

It's just like saying, what is 0 - 2x? It's just -2x. You don't have to have x's to subtract x's.

Answer 33

Okay, so 12/-3 is 4 and 2x/-3 is ? the hardest part for me is doin things with the x and y!? I don't understand how to divide with an x there! Sorry if I am bothering you too much

Answer 34

No, not at all, but you definitely need some practice so you don't make the small errors :)

12/(-3) is equal -4, not just 4.

2x/(-3) is the same thing as saying "negative two thirds times x"
2x/(-3) = -(2/3)x and remember, that stuff in front of x becomes your slope, so your slope is -2/3

So use that slope of -2/3 and find the perpendicular slope as the negative inverse (neg, then flip). With the perp slope and the point they gave you, write the point slope line, then simplify to get the y = mx + b form.