Question

Write the slope-intercept form of the equation parallel to y = 7x + 2, which passes through the point (1, -3).

Answer 1

OK... first, what's the point-slope form of a line?

Answer 2

Sorry, I mean, the slope-intercept form.

Answer 3

i dont know what that is either..

Answer 4

OK ... I guess let's do this one now. The slope-intercept form is, like in the other problem,

y - y0 = m(x-x0).

Now they're telling you it's parallel to the other line, which means it has the same slope, or 'm' value, which is 7. So can you substitute in m=7 and rewrite the equation, what do you get?

Answer 5

y-y0= 7(x-x0? ?

Answer 6

Yes! great! Now the point it passes through is (1, -3). That's your x0 and y0. So let's do x0 first. Take the '1' and put that in for 'x0'. What do you get? (Start with the equation you wrote just now, with the 7 already in it.)

Answer 7

erikasipe, welcome to OpenStudy. Just a heads up - the next time you evade the language filters on a thread we'll be forced to issue you a suspension. Please keep the language clean. Thanks! Best of luck!

Answer 8

so.. y-y0= 7(x-x1?

Answer 9

Almost, you're close. The entire thing that says "x0" is the thing you're replacing. So it is
y-y0 = 7(x-1).

Now there's just one thing left to do, and that's replace "y0" with "-3". This one is a little tricky, because the two negative signs cancel. What do you get?

Answer 10

y-3= 7(x-1) ?

Answer 11

So close. Remember, it's "y - y0", but since y0 is -3, you get "y - -3". And two negatives make a positive. So it's
"y + 3 = 7(x-1)"
does that make sense so far?

Answer 12

kinda.. it's kinda confusing but i'm getting there

Answer 13

this may sound corny but I'm really proud of you for trying.

Answer 14

I want to appoglize for being a rude & disrespectful. You didn't deserve that, I'm truly sorry.

Answer 15

That's OK, we all have our moments. OK, so now we've got
y + 3 = 7(x-1), but the problem asked for what's called "slope-intercept" form, which means just y is on the left, and everything else is on the right. So your answers probably all look like

y = 4x + 4 or something?

Answer 16

So what we're going to do is convert the answer that we have so far into something that looks like the answer they want.

Answer 17

Okay. so what's next?

Answer 18

A. y = 7x - 10
B. y = -1/7 x + 2
C. y = 7x - 3
D. y = -7x + 10
these are the anwsers

Answer 19

so the first thing we do is expand out the thing on the right. On the right it says 7(x-1) and what that means is to multiply 7 times x-1. The way we do that is split the "x-1" into two parts -- the x, and the -1, and multiply 7 by each.

So when we multiply 7 times x, what do we get?

Answer 20

-7?

Answer 21

You're jumping ahead of me a little :-). 7 times -1 is -7, yes! But 7 times x is just plain old 7x. So when we multiply
7(x-1)
what we get is
7x - 7.

So pulling everything together that we've done so far, we have

y + 3 = 7x - 7. One last step, now, is to subtract 3 from both sides. What do you get?

Answer 22

subract 3 from 7?

Answer 23

Well, first we subtract 3 from what's on the left, which is y + 3. y + 3 - 3 is just y.

Now we subtract 3 from what's on the right, so it's -7 (negative 7) minus 3. What do you get?

Answer 24

Once we get the answer I'll explain why we did this.

Answer 25

-10 ?

Answer 26

yes!! that's it!

Answer 27

yay yay yay!

Answer 28

So when you started this step you had

y + 3 = 7x - 7

And when you subtracted 3 from both sides you got

y = 7x - 10.

That's the answer!

Answer 29

wait why isn't the 7 a -7?

Answer 30

Because, what they wanted was just 'y' on the left side, and everything else on the right. So the way we got that was by subtracting 3 from both sides. That left plain old 'y' on the left, and changed the -7 to a -10 on the right.

Answer 31

can you help me with one more just so i get it?

Answer 32

Sure.

Answer 33

Write the point-slope form of the equation passing through (5, -1) with a slope of 6.
A.
y-1=6(x+5)
B.
y+5=6(x-1)
C.
y+1=6(x-5)
D.
y-5=6(x+1)

Answer 34

OK, well let's start again with the basic point-slope form, which is:

(y - y0) = m(x-x0).
Just like before, x and y will stay there. x0, y0, and m will all be changed to the numbers for the line we want.

'm' is the easiest one. Remember, that's the slope. So, what do we put for m?

Answer 35

6?

Answer 36

yes! So, rewrite the equation with '6' there for 'm', what do you get?

Answer 37

so.. (y-y0 = 6(x-x0)

Answer 38

i forgot a parenthesis opps..

Answer 39

YES! you'll be an expert soon :-). Now, the point they gave you is what tells you the (x0, y0). So, what should we put in place of x0?

Answer 40

5?

Answer 41

yes! so what does the equation look like now?

Answer 42

you are doing so well!

Answer 43

(y-y5) = 6(x-x0) ?

Answer 44

The '0' that's in x0 and y0 are confusing you, so let's call them something different, like "Xpoint" and "Ypoint". Let's say the equation is:

(y - Ypoint) = 6(x - Xpoint).

Now, we were given Xpoint of 5, so what does the equation look like after we put it in?

Answer 45

(y-5) = 6(x-x0) ?

Answer 46

Very close, but remember 5 is the X part, not the Y part.

Answer 47

(y-y0) = 6(x-5) ?

Answer 48

yes! You're almost there! now just one last thing, which is to put in -1 for Ypoint. But remember there's an extra minus sign in there!

Answer 49

i forgot! what do you do with minus signs?!

Answer 50

Well remember, the basic part of the equation is (y - y0), so if y0 is regular "8", y - y0 becomes y - 8. But if y0 is -8, when you put it in the equation you end up with y - -8. There are two minus signs there! So they cancel out and become a plus sign.

Answer 51

Wow, this is impressive! Good job! :D

Answer 52

I know, she's doing great!

Answer 53

You're doing great too!

Answer 54

:-)

Answer 55

(y-8) = 6(x-5) ? maybe..

Answer 56

Sorry, I confused you with my example... in the actual problem you're solving, so far you have

(y - y0) = 6(x-5), and the point is (5, -1). That means y0 is -1. But remember, that gives you a double minus sign. So what do you get?

Answer 57

(y-1) = 6(x-5) ?

Answer 58

Clooooose, but since y0 is -1, you'd get (y - -1) on the left. And remember, double minus signs like that cancel out and become a + again. So what would it be?

Answer 59

why do you get two negitiaves?

Answer 60

Well, the first one comes from the equation itself, which says (y - y0). The second comes because the point they gave you as part of the question was (5, -1), which means x0 is 5, and y0 is -1. So the -1 has its own negative sign already -- that's the second negative.

Answer 61

If they'd given you the point (5, 1), then the 1 doesn't have a negative sign, so it would become (y - 1) in the equation. But since the point they gave you is (5, -1) there's a second "extra' negative sign.

Answer 62

oh okay.. so (y--1) = 6(x-5) im not so sure..

Answer 63

Yes, you're really close! And remember when you have a "double negative" like that, the "--" becomes "+". So what's it become?

Answer 64

(y1) = 6(x-5) ?

Answer 65

Almost ... remember, it becomes a "+", so it's

y + 1 = 6(x-5).

Answer 66

and that's the answer!

Answer 67

yay your amazing!

Answer 68

thank you so much <3

Answer 69

you're very welcome, and can I say, I'm really impressed that you really seem to want to learn. You just need to find people -teachers, or parents, or people on openstudy - who have time to really teach you.

I know math can make you FEEL "dumb", but you're not. You're just not good at math yet!

Answer 70

i know! thank you so much.

Answer 71

you're welcome, and have a good evening. see you later!

Answer 72

you too!