Question

I DO NOT understand the algebra that I am doing and would GREATLY appreciate step by step help if anyone would help me. The equations is:
Graph the line passing through the given point and having the given slope. Give the slope-intercept form of the equation of the line if possible. (1,-2), m=-3/5
The point-slope form of the equation of a line with slope m passing through the point is the part I really can't figure out. I don't understand how to distribute the properties when fractions are involved. Will anyone please help me???

Answer 1

Ok, well point slope is just:

\[y-k = m(x-h)\]

Where m is the slope, and (h.k) is any point on the line.

Answer 2

given a point P(x,y) and a slope m

y-Py = m(x-Px)

Answer 3

For this problem you would have:
\[y-(-2) = -\frac{3}{5}(x-1)\]

And to get slope intercept from that you just solve for y.

You are having trouble distributing the fractional slope?

Answer 4

y-(-2)=-3/5(x-1) is where I get stuck because I do not understand the distributing to get to y= for the slope-intercept form of the equation of the line.

Answer 5

Ok, so to distribute you just multiply x and -1 by -3/5

Answer 6

i tend to perfer my version of the slope intercept form;

y = m(x-Px)+Py which simply skips a few steps of algebra

Answer 7

Yeah, but the problem is with distributing fractions which will come up in more places than just this.. ;p

Answer 8

\[y-(-2) = -\frac{3}{5}(x-1)\]\[\implies y -(-2) = -\frac{3}{5}(x) - \frac{3}{5}(-1)\]

Right? That's just simple distribution. Is the question how to do the multiplication of a fraction and a non-fraction?

Answer 9

That is where I am completely stuck!

Answer 10

Ok well when multiplying a fraction and a whole number just multiply the whole number by the numerator. Then simplify.

\[\frac{a}{b}(c) = \frac{a\times c}{b}\]

Answer 11

For the x you can actually just leave it as \[-\frac{3}{5}x\]

Answer 12

If I type out the problem that I am working on now, would you mind looking at the steps to see if I am doing them correctly?

Answer 13

Not at all.

Answer 14

OK, I started out with (1,2), m=-1/4. After plotting the line, I got the other point which is (5,-3). Now I have to figure out the slope-intercept form of the equation of the line.

Answer 15

You don't need to get another point if you are given the slope

Answer 16

Just plug it into the point slope formula.

Answer 17

Now the book says to use the formula, (y-y1)=m(x-x1)

Answer 18

Right, m is the slope. y1 is the y part of your point and x1 is the x part of your point. You don't need a second point.

Answer 19

y-2=-4/3(x+3) and here's where I get totally stuck!

Answer 20

Would you mind explaining the steps from here?

Answer 21

That's a different line..

Answer 22

Which one are we working on

Answer 23

That is the way the book has it written for the above problem that we have been working on.

Answer 24

Oops! That was the example. I'm getting mixed up going back and forth.

Answer 25

"I started out with (1,2), m=-1/4"
\[\implies y-2 = -\frac{1}{4}(x-1)\]

Answer 26

That is the type of form that the problem should be in.

Answer 27

OK, thank you. This is where I don't understand the multiplication and subtraction to isolate y=.

Answer 28

Ok so start by distributing the -1/4

Answer 29

y-2=-1/4x-1/4?

Answer 30

Close.
\[-\frac{1}{4}(-1) = \frac{1}{4}\]

Answer 31

OK so y-2=-1/4x+1/4?

Answer 32

Right

Answer 33

Next would be, y-2-2=-1/4x+1/4-2?

Answer 34

No, because y-2-2 = y-4

Answer 35

OK, y-2+2=-1/4x+1/4+2? to isolate y

Answer 36

Correct

Answer 37

How do I subtract on the right side of the equation?

Answer 38

You mean add?

Answer 39

Yes, sorry.

Answer 40

\[2 = \frac{8}{4}\]\[\implies \frac{1}{4} + 2 = \frac{1}{4} + \frac{8}{4} =\ ?\]

Answer 41

You need to review addition and multiplication of fractions and whole numbers.

Answer 42

http://www.khanacademy.org/video/adding-fractions-with-unlike-denominators?playlist=Developmental%20Math

Answer 43

http://www.khanacademy.org/video/multiplying-fractions?playlist=Developmental%20Math

Answer 44

I think those will help you a lot with this

Answer 45

Thank you so much for your help.

Answer 46

Would the y slope-intercept form of the equation of the line be y=-1/4x+8/4 or would I simplify?

Answer 47

No, that's not right. 2 = 8/4, 2 + 1/4 = 8/4 + 1/4 = 9/4

Answer 48

y=-1/4x+9/4

Answer 49

Yes. That's it.

Answer 50

y=-1/4x+9/4, when I input it, its says that is incorrect.

Answer 51

Careful with the parens.

Answer 52

Technically it should be y=(-1/4)x + (9/4)

Answer 53

Thought the parens on the last term don't matter. If it's still claims that's wrong then you have something wrong with the original problem.

Answer 54

it says the correct answer is y=-1/4x-7/4

Answer 55

Then you wrote the problem wrong.. Was it by chance:

m = -1/4 point is (1,-2) ?

Answer 56

That is why I am not understanding the distribution. Every problem is like this and you enter the steps one at a time and it has been correct up to this point by the way we did the problem.

Answer 57

What we did was correct for the problem you stated. I think you miss-stated the original problem.

Answer 58

The answer they gave would be correct if the point was (1,-2) not (1,2) as you said originally.

Answer 59

Oh my gosh, you are right. It was -2.

Answer 60

So the distribution is fine. You understand ok. You just have to make sure you're solving the right problem ;p

Answer 61

Lol, sorry. I am getting mixed up because every time I look at the "help me solve this" section, after I look at it, it then changes the problem I have to solve.

Answer 62

np. Did you want to try another one?

Answer 63

I want to double check this one since I got the negative wrong but I am going to try to do the whole problem and see if I did it correctly. Here we go....

Answer 64

(y-(-2))=-1/4(x-1)

Answer 65

y+2=-1/4x+1/4?

Answer 66

y+2-2=-1/4x+1/4-2?

Answer 67

sorry one sec.

Answer 68

How much have I messed up so far, lol?

Answer 69

Yes, that's right so far.

Answer 70

OK, here comes the part that gets me every time!!!

Answer 71

y=-1/4x+2/4???

Answer 72

Is 2 more than 1/4?

Answer 73

Which would you rather have.. 2 pies, or 1/4th of a pie.

Answer 74

Well 2 pies but I don't know if that is right, should it be simplified to 1/2?

Answer 75

Hold on. You've made a mistake. I'm just trying to show you how you can tell.

Answer 76

Do I add 2+1 of the fraction which would make it 3/4 instead of 2/4?

Answer 77

If 2 is more than 1/4th, then if you have 1/4 and you subtract 2 will the result be positive or negative?

Answer 78

Negative, I think.

Answer 79

Right, but your answer was positive.

Answer 80

2 = 8/4

So you have 1/4 - 2. That's the same as 1/4 - 8/4. What is 1/4 minus 8/4?

Answer 81

7/4

Answer 82

I'm sorry that I am terrible at this and I appreciate your patience very much!

Answer 83

-7/4

Answer 84

if you have 1 fourth and you take 8 fourths way you will be at -7 fourths.

Answer 85

So on mine, would it be 1/4-2=-1/4

Answer 86

No..

Answer 87

2 is 8 fourths

Answer 88

\[\frac{2}{1} = \frac{8}{4}\]

Answer 89

So the problem you're having here is addition and subtraction of fractions.

Answer 90

You need to study this more.

Answer 91

If I have 1/4th of a dollar. And you tell me that I owe you two dollars. I can pay you my 1/4 and I'd still owe you 1/4 - 8/4 = -7/4ths of a dollar.

Answer 92

http://www.khanacademy.org/video/adding-mixed-numbers-with-unlike-denominators?playlist=Developmental%20Math

Answer 93

Watch the video's I have linked. They should help.

Answer 94

The problem you're having doesn't have anything to do with what you're learning about right now. You are stuck on something you're supposed to have learned already, but it got missed. You have to go back and learn this and everything else will become much much easier.

Answer 95

I have to go. Good luck, and let me know if you want to work on this more later.