Question

The intersection point of the graphs of the following system of equations has an x-coordinate of 3 and a y-coordinate of 24. What information does this intersection point provide ?
y - x = 21
y = 8x

A. The solution of the system
B. The slope of the graphs
C. The y-intercept
D. The constant of proportionality

Answer 1

Is the "y-x=21" and "y=8x" provided in your problem, or is that part of your work to solve it?

Answer 2

It's part of the problem

Answer 3

Ok, and is it one of the questions that may have multiple answers?

Answer 4

Wym ?

Answer 5

Could you rephrase that?

Answer 6

Wat u mean by wat u said before ?

Answer 7

Does your question state that multiple answers could be correct, or is it a standard multiple choice question with only one solution?

Answer 8

It's a standard multiple choice question

Answer 9

Ok, let's ignore the two given slope-intercept formulas for the moment. Does the X and Y coordinate ALONE give us the constant, also known as "k"?

Answer 10

Yes

Answer 11

I can see why you'd think that, but unfortunately it does not. If you say yes because the formula for k is k=(y/x), then you might mistakenly put intercepts as your x and y values, but you have to get those variables from solving for x and y, given a specific set of equations, and neither of your given equations fits that bill.

Answer 12

So let's try the next possibility. Does the given intersection point of (3,24) provide us with a y-intercept?

Answer 13

Yes

Answer 14

Explain how please. In order to help you understand why the right answer is right, I need to know your thought process for this one.

Answer 15

I'm guessing the y-intercept is 24 because it's on the y-axis

Answer 16

Is that right ? @noseboy908

Answer 17

It depends how you say that it's on the y-axis. More exactly, the y-axis is used for the ordered pair to simply say how high on the y-axis the point is, but you have to take into account the x value too. Understand?

Answer 18

Wat I mean is so the coordinates are (3,24) so the 3 would be where the x-axix is and the 24 is where the y-axix is but I understand wat ur trying to say

Answer 19

Ok, now let's go to the next possibility. Let's keep it simple. Can you determine slope of a line when all you know about that line is a single point on it?

Answer 20

I don't understand

Answer 21

How does one find the slope of a line?

Answer 22

Did you mean can we find the slope of a line knowing only one of the points ?

Answer 23

Exactly!

Answer 24

Oh well then no

Answer 25

Good, I was hoping I'd not have to defend that fact! Now, finally, look at the last possibility for an answer. When we have two lines that intersect at one or more points, what do we call those points?

Answer 26

Intersection

Answer 27

Correct, but can you think of any other terms?

Answer 28

No

Answer 29

I'll tell you, as you may have never heard it before. Another term for the intersection of two lines, given the right question, is the "solution", therefore, when you have two or more of them, you can have multiple solutions, but that's getting into higher math. So, what does that leave us for an answer?

Answer 30

Ohhhhh yea I'm sorry I forgot and so the answer would be C. The y-intercept

Answer 31

Ok, we just determined that the intersection of two points is called what?

Answer 32

(In this case)

Answer 33

The solution

Answer 34

And which answer is that?

Answer 35

Exactly!! Now, be honest with me, do you understand why the other answers are not correct?

Answer 36

Yes .. But can you explain to me why the answer isn't C. Please ?

Answer 37

Of course! Firstly, it's imperative to note that ALL y-intercepts have an inherent x-value of 0. That's because if was any different, then the point would actually fall x units right or left of the axis!

Answer 38

Ohhh I understand .. Thanks so much ! @noseboy908