Question

A line has a vertical change per unit of horizontal change of three-halves and passes through point two comma two. Which is another point on the line?

A) 5,4

B) 4,6

C) 4,5

D) 6,4

Can You Explain this to me? Thanks!

Answer 1

so are you familiar with point slope form of a line?

Answer 2

Yes but I have trouble with it, but maybe when you explain ill be more familiar.

Answer 3

ok, so can you write the formula for me please?

Answer 4

(x1, y1) and (x 2, y 2) is that right?

Answer 5

not quite, but I appreciate you trying :) so the formula is: \[(y-y_0)=m(x-x_0)\]

Answer 6

your welcome and ok

Answer 7

\(y_0~and~x_0\) are the coordinates of the point you are given in this case

Answer 8

Do you follow?

Answer 9

\(\bf slope = \cfrac{rise}{run} \implies \cfrac{\text{vertical change}}{\text{horizontal change}}\)

Answer 10

I just followed you. and ok.

Answer 11

Thanks for the formula thats easier to understand.

Answer 12

So do you know what the m represents?

Answer 13

The m represents..three-halves ?

Answer 14

That is correct in this case, but can you tell me in general what it represents?

Answer 15

Oh sorry its the horizontal change, correct?

Answer 16

not quite, think about the name of the formula

Answer 17

slope?

Answer 18

That is correct.

Answer 19

Sorry about that I struggle in summer school math

Answer 20

So as jdoe supplemented, slope can be described in a lot of ways.

Answer 21

it's ok, it happens all of the time

Answer 22

So can you guess what our formula will be for the line?

Answer 23

Yes I saw (: So do I do this.. Slope = 3 over 2 ?

Answer 24

yep. :) so can you put that into our formula?

Answer 25

what do you mean by that?

Answer 26

remember the point-slope formula I listed above? That can be used to give the equation of the line. This is something that we need to solve the problem

Answer 27

So can you fill in the missing information?

Answer 28

(3 - 2) =m ?

Answer 29

not quite. so let's take a step back, the slope =m=?

Answer 30

2,2 ?

Answer 31

No, what did you say before was the slope?

Answer 32

3 over 2

Answer 33

so m=?

Answer 34

m = 3 over 2

Answer 35

correct so what is \((x_0,y_0)\)? also called any point on the line?

Answer 36

the point on the line is... (2,2) ?

Answer 37

yes! that is correct. now, can you plug the vales into the eq? \[ (y-y_0)=m(x-x_0)\]

Answer 38

OH! now I get it ok so (2 - 3) =m(2 -2) ?

Answer 39

no, no, not quite remember m=?

Answer 40

oh the other way around like.. (3 -2) =m(2-2) ?

Answer 41

no, just answer this. m=?

Answer 42

3 over 2

Answer 43

\(x_0=?\)

Answer 44

2

Answer 45

\(y_0=?\)

Answer 46

2

Answer 47

now exchange the values you just listed for their counterparts in the eq. \[(y-y_0)=m(x-x_0)\]

Answer 48

(y - 2) =m(x -2) but the net part I dont know yet

Answer 49

net part?

Answer 50

next*

Answer 51

so you have not inserted one value, m can you please replace this as well

Answer 52

I do not know what y & x are yet

Answer 53

You don't need those

Answer 54

you already know m you just put it in

Answer 55

Ok so I did the rest right.

Answer 56

yes

Answer 57

Now what?

Answer 58

all you do is plug in the corresponding values (x,y) do not have any values. Now write the eq with the substitution for m.

Answer 59

so x&y stay x&y

Answer 60

I dont understand

Answer 61

what don't you understand?

Answer 62

what do I do next? I already did the expression with the (2,2) in and I left Y and X blank so now what..?

Answer 63

You literally just put \(\frac{3}{2}\) where the m is in the eq. that's it.

Answer 64

you have not replaced it yet

Answer 65

that is the eq of the line

Answer 66

http://www.purplemath.com/modules/strtlneq.htm for reference

Answer 67

so.. (3 - 2) =m(2-2) ?

Answer 68

NO! what is m=?

Answer 69

the m in the eq that you keep typing as an m

Answer 70

I said x and y stay there don't rewrite them

Answer 71

ok then (y - 2) =m(x - 2)

Answer 72

replace the m with it's value

Answer 73

do not write an m

Answer 74

so just write 3 and 2 where the 2's are and dont write m

Answer 75

no

Answer 76

what does m=?

Answer 77

three-halves

Answer 78

so instead of writing m write that.

Answer 79

ok (y - 2) =3 over 2 (x - 2)

Answer 80

yes!

Answer 81

ok now

Answer 82

ok now. just see which points satisfy this eq.

Answer 83

6,4?

Answer 84

so if x=4 what does y=?

Answer 85

6

Answer 86

no,

Answer 87

so we get the eq. \(y-2=\frac{3}{2} (4-2)\)

Answer 88

yes

Answer 89

just solve

Answer 90

what is 4-2=?

Answer 91

2

Answer 92

now what is \(\frac{3}{2}(2)=?\)

Answer 93

3

Answer 94

right. so we have y-2=3

Answer 95

so y=?

Answer 96

5 so its 5,2 ?

Answer 97

what?

Answer 98

where did you get that?