Question

What is the equation of a line through (2,4) with the x-intercept twice the y-intercept?

Answer 1

What i tried to do here was, make a second point, so i did (2x,y) as my second point and then used two point form? i am not sure though, please help

Answer 2

That sounds pretty good. Good effort! I think there's something a little more tricky going on that defeats that approach though. :)

Answer 3

The problem is that the "x-intercept" and the "y-intercept" are actually two separate points! That is (x, 0) and (0, y).

Answer 4

So, we really have three points to think about: (2,4), (x,0), and (0,y). Make sense so far?

Answer 5

oh, i lagged, okay okay yep i didnt notice

Answer 6

But we still need to use the fact that the x-intercept is "twice" the y-intercept somehow... before I give it away, any ideas that come to mind? It's not necessarily obvious, so don't feel bad if you get stuck. Let me know what you think. :)

Answer 7

hmm, i think it would be (2x,0) (0,y)

Answer 8

That is a very logical choice... BUT (you knew that was coming :) ) this isn't the "mathy" way to say it. If you think about it, even though you have said 2x and y, there isn't anything that really tells me that y is related to x at all! I could pick 2*2 for x-intercept and 1920 for the y-intercept and your definition couldn't stop me. Tricky... tricky... :)

Answer 9

What you want to say is that x = 2k, and y = k. They are based on the same choice (k). Then we get (2,4), (2k, 0) and (0, k). This shows that the x and y-intercept are based on the same number and are related.

Answer 10

Now, if I say x = 2*2, then k = 2, and I am forced to pick y = 2 also. Any questions? It's a little confusing at first.

Answer 11

ohhh, okay i get it ! :D and i can see the next steps now :)

Answer 12

so since the line passed at (2,4) i can use the other 2 points (2k,0) and (0,k) to get an idea for the slope right? or... do i still use (2,4)?

Answer 13

You can sort of do it both ways! Lines are nice and straight, so you have many ways to find the slope. Try the way that makes the most sense to you first (and worst case double check by doing it the other way... ouch... the pain!). :)

Answer 14

i was thinking of using the two point form, so ill use (2k,0) and (0,k); (x1,y1) (x2,y2) respectively and then substituting the point (2,4) into the (x,y) to get the value of k, do i have to substitute the value of k to the points (2k,0) and (0,k) after i get it? and then get the equation from there using two point form again?

Answer 15

I think you can do it that way, that should work.

Answer 16

I found the slope directly just by looking at (2k, 0) vs. (0, k). Rise is -k, run is 2k, so slope = -k/2k = -1/2.

Answer 17

ah, sorry if it took me a long time to respond, i had to move to a different internet cafe, but i get it so ill use the slope and then input the points (2,4) in y = mx +b :D

Answer 18

Yep, looks good.

Answer 19

final answer i got is y = -1/2x + 5

Answer 20

As did I... we can check by making sure that (2,4) works, and by testing x = 0 and y = 0 separately. I did and it does work. Hooray for math! ;)

Answer 21

Nice work, this was not an easy one.

Answer 22

whooo !! :D thanks !