Question

need to find the equation of the line having the given slope and containing the given point

m=5, (8,4)

Answer 1

Are you familiar with the point slope formula? It basically does exactly what you're asking for here..

Answer 2

yes, but for some reason I blank looking at it

Answer 3

Ok, so lets say you are given a slope (m) and a point (h,k)

Then the equation for the line going through that point having that slope is:

\[y-k = m(x-h)\]
That's it. In this case (h,k) is (8,4) and m is 5. Find & replace.

Answer 4

Give it a try?

Answer 5

im working at it but im going to warn u I really suck at this...lol
i draw blanks

Answer 6

There's nothing to do. What is h? what is k? what is m?

Answer 7

i know im just writing out

Answer 8

Well can you tell me really fast what h is?

Answer 9

8

Answer 10

So instead of \[y-k = m(x-h)\] we have \[y-k = m(x-8)\]

What is k?

Answer 11

4

Answer 12

So we have:
\[y-4 = m(x-8)\]

What is m?

Answer 13

5

Answer 14

So we have:\[y-4 =5(x-8)\]

And we're finished.

Answer 15

see i know its easy but for some reason my brain doesnt connect with math. Thank u so much

Answer 16

When they say 'h' is '8' it literally means you can take one, and put in the other instead and it means the same thing.

Answer 17

i need to keep u around

Answer 18

u make sense

Answer 19

Most people just get themselves all stressed out when it comes to math. There's nothing tricky about it. They try to dress it up with funny symbols, but once you know what it means it's really very straight forward.

Answer 20

Don't panic. You can do this. You are good at it, you just confuse yourself or put up roadblocks.

Answer 21

very true. I have always stressed out when it came to math because its the only thing I copuld never do for whatever reason

Answer 22

All math is just ordered thinking. Has almost nothing to do with numbers.

Answer 23

I could do it at work but I cant do it for school

Answer 24

You can. You have to believe that you can do it, and that it's not as hard as you think. =)

Answer 25

95% of peoples issues with math have to do with social and environmental training and stress. Almost nothing to do with aptitude.

Answer 26

I believe I can do it but I know I cant...lol
I get stuck on stupid

Answer 27

ever since I can remember I could never do math

Answer 28

im jinxed when it comes to Math....lol :)

Answer 29

That's the problem right there though. Not that you cannot do it, but that you believe you cannot. You must change the way you think about math. It is not a chore. It's not a punishment. It's just a way of thinking about things (everything) and you honestly do it all the time without realizing it.

Answer 30

I do it at work everyday with no problem but for some reason because I HAVE to do it for school, i freak out. You are right about that

Answer 31

So lets look at another problem and try not to freak out. Or if you don't have any, I can make some up for you. You're studying lines?

Answer 32

yes, im studying lines. Let me see, I may have another

Answer 33

Even if it's similar it's good to practice what you know.

Answer 34

for that last one though I need the y= part

Answer 35

really? Ok then. What do you need to do first?

Answer 36

Actually hang on.

Answer 37

We can make a new formula! That will make this easier the next time you have to do it.

Answer 38

awesome!

Answer 39

So lets see.. we started with a slope and a point. Lets call the slope m and the point (h,k) again.

What was the point slope formula?

Answer 40

y=mx+b

Answer 41

That's the slope intercept formula.

Answer 42

Same line, but different arrangement that makes some things easier to see.

Answer 43

thats what it asks me to put the answer in though

Answer 44

That's fine.. That's where we want to end up. I'm saying where did we start?

Answer 45

What was the formula I was having you plug in h,k and m into?

Answer 46

y-k=m(x-h)

Answer 47

Indeed. So now we need to have the y by itself to find y = mx + b form. What do we need to do?

Answer 48

i know we need to subtract something from both sides

Answer 49

That's right. (or add perhaps). What can we add or subtract from both sides to get the y by itself?

Answer 50

What specifically do we need to get rid of on the left hand side?

Answer 51

k

Answer 52

Right. So what do we do to get rid of the -k ?

Answer 53

add

Answer 54

add what?

Answer 55

k (4)

Answer 56

We're just dealing with h , k and m now because then we won't have to re-do all this when we have another problem and they tell us h,k is 20,30 etc.

Answer 57

So if we add a k to both sides, what will we get?

Answer 58

What will we get on the left side (the whole reason we did it)?

Answer 59

y

Answer 60

Right, and on the right side? We still have what we had before +k right?

Answer 61

So rewrite the equation?

Answer 62

y=5(x-8)

Answer 63

no no. Where did those numbers come from?

Answer 64

Just h, k, and m.

Answer 65

y = m(x-h) + k

Answer 66

Right?

Answer 67

o yes sorry

Answer 68

So now we just have to simplify the m(x-h) bit into the form we want.

Answer 69

Can you distribute that m to each of the terms?

Answer 70

so am I plugging in numbers now?

Answer 71

No.

Answer 72

Wait till we get the form we want. Then plug in the numbers after all the algebra is done.

Answer 73

Distribute,

m(x - h) = ?

Answer 74

k

Answer 75

m(x-h) = mx - mh

Answer 76

So we have:
y = mx -(mh - k) = mx + b

So b = -(mh - k)

Answer 77

i couldnt type it fast enough

Answer 78

So now we can plug in any numbers you have for m, h, and k to find your equation.

Answer 79

y=-4(5x-8)? or something close

Answer 80

\[y = 5x -(5(8) - 4)\]
\[\implies y = 5x -(40 - 4)\]\[\implies y = 5x - 36\]

Answer 81

wouldnt it be y=5x+36