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A line passes through (2, 8) and (4, 12). Which equation best represents the line?
y = 1 over 2x + 6
y = 2x + 7
y = 2x + 4
y = 1 over 2x + 10

- anonymous

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- eyust707

The formula for a line can look like this|dw:1437333815430:dw|

- eyust707

The only thing we need to do is figure out what y1, x1 and m is.

- anonymous

I do not understand the formula though :/

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- eyust707

Well if we figure out these three numbers we can plug them in, simplify and we'll have our answer |dw:1437333928564:dw|

- anonymous

When you say plug in numbers do you mean guessing them?

- eyust707

Nope we need to calculate them based on the two points given.
"m" represents the slope of a line.
If you are given two points the best way to fin the slope is to calculate "the change in y"/"the change in x"

- anonymous

What do you mean by that change in Y and X?? Sorry if I sound clueless :/

- eyust707

(2, 8) and (4, 12) are our points.
Whenever we see two number in parenthesis separated by a comma this is telling us where a point is located on a graph. the first number tells us how far over to go left and right (your x value). The second number tells us how far to go up and down (your y value).
|dw:1437334303980:dw|
To get to point (2,8) you would start at the origin go over 2 spaces then up 8.
|dw:1437334574867:dw|
If you have two points, to get from one to another you also need to go over by a certain amount and up by a certain amount.
|dw:1437334702484:dw|
In this case, to get from the first point to the second, we have to go over 2 and up 4
See y goes from 8 to 12. 12 - 8 = 4 so change in y is 4
x goes from 2 to 4. 4-2 = 2 so change in x is 2
change in y/ change in x = 4/2
4/2 = 2
so m = 2

- anonymous

Sorry I resent that message

- anonymous

Okay but It askes me which best represents and equation not the answer

- anonymous

asks~

- eyust707

Yes yes we are getting there, whats more important however than finding the answer is for you to develop an understanding that way you can find all the rest of the answers by yourself!

- eyust707

Do you understand how I got m?

- anonymous

You had changed Y and then X=4/2 so then 4/2 equals 2 so M=2

- eyust707

awesome! now you know how to find "m" or "slope" if given two points!
the only other things we need is y1 and x1
Well thats easy, y1 is the y value of the first point and x1 is the x value of the first point.

- eyust707

What is the y value of (2,8) ?

- anonymous

Okay so would I divide 4,12 by 2 or something?

- anonymous

lol sorry wrong number

- eyust707

What is the y value of (2,8) ?

- eyust707

*hint* i explained this and gave you the answer earlier in this thread ;)

- anonymous

Okay but Idk how you find that?

- eyust707

Whenever we see two number in parenthesis separated by a comma this is telling us where a point is located on a graph. the first number tells us how far over to go left and right (your x value). The second number tells us how far to go up and down (your y value).

- anonymous

Ohhh Y is 4

- eyust707

change in y is 4

- eyust707

But the y value of the point (2,8) is simply 8

- eyust707

so y1 = 8

- anonymous

okay

- eyust707

what is the x value of the point (2,8) ?

- anonymous

I thought x was 4,12?

- anonymous

Wait X is 2

- eyust707

correct

- eyust707

x1 = 2

- anonymous

Okay

- eyust707

So if we recall:
m=4
y1=8
x1=2

- anonymous

:o would this be C?

- eyust707

Now all we need to do is put those numbers into this equation:
|dw:1437336182607:dw|

- anonymous

:/ It is the only one that has 4 in the answer and 2

- eyust707

|dw:1437336219281:dw|

- anonymous

Because X=2

- anonymous

And Y equals 4

- eyust707

x1 equals 2

- anonymous

So Y=2x+4

- eyust707

All you need to do now is simplify this equation|dw:1437336341302:dw|

- eyust707

|dw:1437336351506:dw|

- eyust707

|dw:1437336364838:dw|

- eyust707

Add 8 to both sides and you are done

- eyust707

oops im sorry m = 2

- anonymous

Wait on the equaton that is represented black?

- eyust707

|dw:1437336473127:dw|

- eyust707

|dw:1437336518614:dw|

- eyust707

add 8 to both sides

- eyust707

|dw:1437336564148:dw|

- anonymous

So the answer is C

- eyust707

yep

- anonymous

Yay thank you

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