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

- kenialove

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- noseboy908

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

- kenialove

It's part of the problem

- noseboy908

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

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## More answers

- kenialove

Wym ?

- noseboy908

Could you rephrase that?

- kenialove

Wat u mean by wat u said before ?

- noseboy908

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

- kenialove

It's a standard multiple choice question

- noseboy908

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"?

- kenialove

Yes

- noseboy908

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.

- noseboy908

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

- kenialove

Yes

- noseboy908

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.

- kenialove

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

- kenialove

Is that right ? @noseboy908

- noseboy908

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?

- kenialove

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

- noseboy908

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?

- kenialove

I don't understand

- noseboy908

How does one find the slope of a line?

- kenialove

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

- noseboy908

Exactly!

- kenialove

Oh well then no

- noseboy908

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?

- kenialove

Intersection

- noseboy908

Correct, but can you think of any other terms?

- kenialove

No

- noseboy908

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?

- kenialove

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

- noseboy908

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

- noseboy908

(In this case)

- kenialove

The solution

- noseboy908

And which answer is that?

- noseboy908

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

- kenialove

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

- noseboy908

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!

- kenialove

Ohhh I understand .. Thanks so much ! @noseboy908

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