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How to find out if a certain point is on a line? watch

1. If I have an equation of a line how can I find if a certain point is on the line?For example y=-2/3x+3/2 show that point (9,-2) lies on that line.
2. Substitute the x values for 9, the y values for -2 and bring it all to one side and it should equal zero.
3. (Original post by Anonymous1502)
If I have an equation of a line how can I find if a certain point is on the line?For example y=-2/3x+3/2 show that point (9,-2) lies on that line.
Substitute the x value into the equation, see what value of y this gives you, and if it is the y-coordinate of the point you are checking out, then it does indeed lie on the line.
4. Put the X and y value into the equation, both sides should come out to be the same if the point is on the line
5. (Original post by Appleorpear)
Substitute the x values for 9, the y values for -2 and bring it all to one side and it should equal zero.
There is a slight problem with this, as you are assuming that the point lies on the line to prove that it lies on the line. Just because you end up with a true statement, it does not mean that you started off witha true statement. False statements can imply true ones, so a true conclusion does not mean that you have a true premise. This is overkill for a simple problem like this, but it's best to avoid this kind of reasoning as a matter or principal.

So, just substitute in the x-coordinate and verify that you get the correct y-cooridnate.
6. (Original post by Pangol)
Substitute the x value into the equation, see what value of y this gives you, and if it is the y-coordinate of the point you are checking out, then it does indeed lie on the line.
so y=-2/3*9+3/2
y=11/2

??
7. (Original post by Anonymous1502)
If I have an equation of a line how can I find if a certain point is on the line?For example y=-2/3x+3/2 show that point (9,-2) lies on that line.

Sub x=9 into it
8. (Original post by Anonymous1502)
so y=-2/3*9+3/2
y=11/2

??
Assuming you have typed the equation out correctly, that point is not on that line (although I think you should have -9/2, not 11/2 - still not on the line!).
9. (Original post by Pangol)
There is a slight problem with this, as you are assuming that the point lies on the line to prove that it lies on the line. Just because you end up with a true statement, it does not mean that you started off witha true statement. False statements can imply true ones, so a true conclusion does not mean that you have a true premise. This is overkill for a simple problem like this, but it's best to avoid this kind of reasoning as a matter or principal.

So, just substitute in the x-coordinate and verify that you get the correct y-cooridnate.
No. You can plug in both coordinates and check that , if it does it lies on the line, if not, it doesn't. There's no assuming it lies on the line in the first place.
10. (Original post by Pangol)
There is a slight problem with this, as you are assuming that the point lies on the line to prove that it lies on the line. Just because you end up with a true statement, it does not mean that you started off witha true statement. False statements can imply true ones, so a true conclusion does not mean that you have a true premise. This is overkill for a simple problem like this, but it's best to avoid this kind of reasoning as a matter or principal.

So, just substitute in the x-coordinate and verify that you get the correct y-cooridnate.
It's not a problem. It would be a prove that question on an exam and either way is perfectly fine.
11. (Original post by Zacken)
No. You can plug in both coordinates and check that , if it does it lies on the line, if not, it doesn't. There's no assuming it lies on the line in the first place.
I agree with that if you first rearrange in the way that you have. But if this isn't done, there is a danger of doing a proof of the kind that ends up with "0 = 0, therefore the original premise is true." It seems far safer to start with one coordinate and obtain the other rather than insert them both in the first place.
12. (Original post by Pangol)
I agree with that if you first rearrange in the way that you have. But if this isn't done, there is a danger of doing a proof of the kind that ends up with "0 = 0, therefore the original premise is true." It seems far safer to start with one coordinate and obtain the other rather than insert them both in the first place.
From my understanding to solve such questions I insert the x value and the y should equal to the y value that was not inserted?
13. (Original post by Anonymous1502)
From my understanding to solve such questions I insert the x value and the y should equal to the y value that was not inserted?
That's what I think you should do, yes. However, the coordinate you have given does not lie on the line you have given, so there's an error somewhere (possibly in the question you have been set).
14. (Original post by Pangol)
That's what I think you should do, yes. However, the coordinate you have given does not lie on the line you have given, so there's an error somewhere (possibly in the question you have been set).

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