Question

Can someone please check this? I fan and give medals! :)
Which is an equation in slope-intercept form for the line passing through (5, 1) and (–4, 7).
y=2/3x+13/3

Answer 1

@Timelordguy

Answer 2

I don't want to steal Timelordguy's thunder, but to check your answers, just plug in the values 5 and -4 as x into your conjecture (educated answer) and see if the values come out to y = 1 and 7 respectively.

Answer 3

If you need assistance doing that, I am happy to help you.

Answer 4

Yes actually I will need some help doing that. @IParke

Answer 5

So, you believe your equation to be y=2/3x+13/3.
To check your answer, plug in the coordinates you were supposed to have the equation fit.
So, let's take the first coordinate your equation is supposed to satisfy: (5,1)
This coordinate means that when x=5, y=1. Do you follow?

Answer 6

Let's plug those values into your equation and see if the coordinate works.

Answer 7

yes

Answer 8

ok

Answer 9

y=2/3x+13/3
So, for (5,1), this becomes:
(1) = (2/3)(5) + (13/3)

Answer 10

Do you follow?

Answer 11

yes I sorta get it

Answer 12

So all I did was replace y with the 1 in (5,1) and the x with 5 in (5,1)

Answer 13

Is this clear?

Answer 14

Since (5,1) means x= 5 and y= 1.

Answer 15

oh ok yes

Answer 16

Good, now please evaluate the right side of your equation that I used substitution on:
(1) = (2/3)(5) + (13/3)

Answer 17

Tell me what the right side of the equation ends up being
1 = ?

Answer 18

ok um well I just divide 2 by 3 then multiply by 5 and then add 13 divided by 3?

Answer 19

Correct

Answer 20

7.66666666667

Answer 21

Does 1 = 7.667?

Answer 22

I am sorry to report, your answer is wrong.. BUT! I can give you a nice clue

Answer 23

ok

Answer 24

Make your 2/3's a negative, and try it again :)

Answer 25

ok let me try again

Answer 26

1=1

Answer 27

I absolutely believe you know how to do this problem, you just made an error with the sign somewhere along the way :) You should find that 1=1.

Answer 28

Excellent!

Answer 29

great so it was correct?

Answer 30

Now, for the final test, try using substitution with the other point: (–4, 7)

Answer 31

So to recap, so far you've proven that the equation y=-2/3x+13/3 goes through (5,1). You now need to prove that it also goes through the other point, (-4, 7)

Answer 32

Does this make sense?

Answer 33

um yeah it kinda does

Answer 34

Would you like me to walk you through proving that your equation goes through -4, 7?

Answer 35

yes please your an amazing person!!! God bless you because my math skills are terrible!

Answer 36

haha, God bless you too for trying to improve!

Answer 37

So, we are going to use substitution again.

Answer 38

haha thanks!

Answer 39

So, please plug in the coordinate (-4,7) into the equation: y=-2/3x+13/3

Answer 40

so would it be -4=-2/3(7)=13/3?

Answer 41

Hmmm. Let us remember that the x-coordinate comes first in the coordinate pair :)
(x = -4, y = 7)

Answer 42

oh ok duh! so then its 7=-2/3(-4)+13/3

Answer 43

@IParke

Answer 44

Yes! Please evaluate the right side of the equation to see if 7=7!

Answer 45

And if it does, then your equation is perfect :)

Answer 46

Oh my gosh thank you so very much you ARE A LIFESAVER!!!!! :)

Answer 47

Haha, I don't know about that, but I am so happy you're learning. If you are still confused, please let me know, I'll explain all of this to you in plain English.

Answer 48

ok thanks I'll DEFINITELY need your help in the future!

Answer 49

Good luck with your math endeavors!