# Thread: A Graph, A Bug, and a Puzzled Me

1. ## A Graph, A Bug, and a Puzzled Me

This problem was presented to me in my Geometry class but I am certain that this problem must have something to do with Algebra. I hope I can receive help with this for it has stumped me for the past two hours, quite literally. Whatever you can do will help.

Problem: A bug moves linearly with constant speed across my graph paper. I first notice the bug when it is at (3,4). It reaches (9,8) after two seconds and (15,12) after four seconds. Predict the position of the bug after six seconds, after nine seconds, and after t seconds.

I tried working it out and my answer for six seconds is (21,16) and my answer for nine seconds is (30,22). I used a graph to figure those two out.
The last part about t seconds truly puzzles me. I believe that a formula is the answer for that part, but that is all I know. I hope you can help me figure that part out.

If I am wrong or if you have any idea on how to solve this, please help.

Thanks.

2. ## Re: A Graph, A Bug, and a Puzzled Me

You can work out the bug's speed in the x direction and in the y direction, if the speed in the x direction is $S_x$ then after t seconds it will have moved a distance of $S_x \times t$ in the x direction from where it started.

3. ## Re: A Graph, A Bug, and a Puzzled Me

Thanks! I think I sort of get it now. I basically have to find t using that formula.
I have to turn this in tomorrow anyways, so I'm going to hold your answer and hope for the best.