Question

FAN AND MEDAL:



Given the equation y - 3 = one half(x + 6) in point-slope form, identify the equation of the same line in standard form.

x - 2y = -12

y = one halfx

y = one halfx + 6

y = one halfx + 9

Answer 1

@iPwnBunnies

Answer 2

Please Help?

Answer 3

Can you simplify it so only 'y' is remaining on the left side?
\[y - 3 = \frac{1}{2}(x + 6)\]

Answer 4

I don't know. I am unfamiliar with this topic...I don't know how to solve it

Answer 5

.-. Do you know simple algebra, distributive property, and such?

Answer 6

\[ y - 3 = (one~half)(x + 6)\rightarrow y-3=\frac{ 1 }{ 2 }(x+6)\]

Answer 7

All I did here was to write the problem correctly, mathematically.

Answer 8

Not really. That what this is. I'm taking Algebra 1 right now...

Answer 9

Okay. Thank you @mathmale

Answer 10

do I have to distribute the 1/2 ?

Answer 11

What you need to do next is to solve \[ y-3=\frac{ 1 }{ 2 }(x+6)\] for y. You could distribute that (1/2) if you want, but I have a suggestion that might involve less work.

Answer 12

To eliminate that fraction, 1/2, please multiply all terms by 2. Note that (1/2)(x+6) counts as ONE term, not as two terms.

Answer 13

Okay. so do I add 3 to both sides so that y is by itself?

Answer 14

You could do that if you prefer to attack the problem in that order.

Answer 15

Your choice.

Answer 16

Well, how do you recommend? Because I'm not good at this at all... :(

Answer 17

You've got to be willing to experiment and to take risks. Why not do this problem both ways? Then you can decide which way YOU prefer.

Answer 18

Okay. So if I subtract the 3, then would you get:
y= 1/2(x+6) - 3 ?

Answer 19

Kayla, please stop saying derogatory things about yourself such as, "I'm not good at this at all." What you don't know you can most likely learn. Beating upon yourself simply raises obstacles instead of tearing them down.

Yes, that equation is what you'd get, EXCEPT that the sign of your 3 must be positive, not negative. Why?

Answer 20

Actually, you are ADDING 3 to both sides of your original equation, not subtracting 3.

Answer 21

Oh yes. Because I am adding so:
y= 1/2(x+6) +3

Answer 22

Very nice.

Answer 23

Then whats the next step?

Answer 24

I'm going to type your equation in Equation Editor for greater clarity. If you know how to use E. E., great; if not, you could either use parentheses or draw your equation in the Draw utility, below.

\[y= 1/2(x+6) +3\rightarrow y= \frac{ 1 }{ 2 }(x+6) +3\]

Answer 25

Now, Kayla, please multiply each of the 2 terms on the right side of this equation by 2 (to remove the fraction (1/2); also multiply the left side of the equation by 2. What do you get?

Answer 26

Is that the blue button with the sigma that says equation?

Answer 27

Yes. Let's go into that a bit later. Please let's solve this equation first.

\[2(y=\frac{ 1 }{ 2 }(x+6) ) \rightarrow ??\]

Answer 28

Multiply each of the two terms within the outer set of parentheses by 2.

Answer 29

\[(2)y = (2)\frac{ 1 }{ 2 }(x+6) +3(2)\]

Answer 30

Good. That boils down to 2y on the left side and (what?) on the right side? I see you've found my oversight. You were and are correct to have included that 3(2) (which I'd neglected to write in).

Answer 31

so:\[2y=2x+12 +6]

Answer 32

\[2y= 2x +18\]

Answer 33

right?

Answer 34

Please look at this again:\[(2)y = (2)\frac{ 1 }{ 2 }(x+6) +3(2).\]
Doesn't (2)(1/2) reduce to 1?

Answer 35

\[(2)y = (2)\frac{ 1 }{ 2 }(x+6) +3(2)\]

Answer 36

If 2(1/2) reduces to 1, then we get:\[2y=1(x+6)+6.\]

Answer 37

check this out and convince yourself that this is correct; if you can't, let's discuss it further.

Answer 38

Wait, wouldn't you multiply the (x+6) by 2 as well?

Answer 39

You already have done that:\[2(\frac{ 1 }{ 2 }(x+6))=\frac{ 1 }{ 2 }(2)(x+6)=??\]

Answer 40

Try bringing it to the for Ax+By+C=0...

Answer 41

Oh okay. So then what do i do? Do i divide everything by 2 so that the y is alone again?

Answer 42

Explain? @Yajnesh_Joglekar

Answer 43

Multiply the original eqn by 2...

Answer 44

Tell me what u get

Answer 45

Let me ask you this: What is the value of 2(1/2)? of (1/2)(2)?

Answer 46

2/2 which is 1. And 2/2 which is 1.

Answer 47

Ans this !... :O

Answer 48

I continued on the math and I came up with this:
x - 2y = -12
is it right?

Answer 49

U got it.. :P :D

Answer 50

Awesome! I was kinda confused at first..but I think what you told me about finding a way to better understand it myself helped. @mathmale Thanks to both of you! @mathmale and @Yajnesh_Joglekar

Answer 51

Let me summarize:
\[2(\frac{ 1 }{ 2 }(x+6))=\frac{ 1 }{ 2 }(2)(x+6)\]becomes\[2(\frac{ 1 }{ 2 }(x+6))=\frac{ 1 }{ 2 }(2)(x+6)=x+6. \]
So then we end up with 2y=x+6+ 6, or 2y=x+12.

Since our job is to solve for y, please divide both sides of this latest equation by 2. What do you get?

Answer 52

Is the answer I got not right? And @mathmale May you help me a little more?

Answer 53

Remember, Kayla, your objective here is to SOLVE FOR y.

Your present result is x-2y=-12, which has not yet been solved for y.

Answer 54

Not necessarily. It's asking for me to identify the equation of the same line in standard form.

Answer 55

Much of our discussion here has consisted of reviews. the actual problem solution is pretty straightforward, once you have the experience:

Actually, you're doing better than I here. I've overlooked that "standard form" until now. Your equation, x-2y=-12 IS already in standard form.

sorry about that.

I'm going to double-check your result quickly, but at first glance I believe it's correct.

What do y ou want to do next? if you have further questions, please post them, one at a time in the "Ask a question" box.

Answer 56

Okay. Thank you

Answer 57

Your result is perfect. congrats!

Answer 58

Both you and @Yajnesh_Joglekar have helped me tremendously. I think i'm beginning to understand this better. And thanks @mathmale ! I wouldn't have been able to find the answer without you! (:

Answer 59

To demo how brief the actual problem solution can be:\[y-3=\frac{ 1 }{ 2 }(x+6)\]Multiply both sides by 2. Result:\[2(y-3)=x+6\]

Answer 60

Haha Wow. I could have been done forever ago lol And I tagged you in a problem

Answer 61

Distribute that 2 over (y-3):\[2y-6=x+6\] Subtract 2y from both sides of this equation, and then subtract 6 from both sides:\[2y-6\] (I'm not finished yet, but if you understand this process and already have the correct answer, let's move on!

Answer 62

I'm good hun (: