TwiddleLab / Math / Functions You Can See
When Two Lines Meet
What you will learn
- Where two lines cross is their intersection.
- At that point both formulas are true at once: same x, same y.
- Reading the crossing off a graph solves two equations together.
How the lesson goes
Ana has 20 coins and saves 5 a week. Ben has 50 and saves 2.
Will Ana ever catch up? Drag the flag to the week you bet, or into never.
Run the weeks.
Each week coins drop into both jars, and both lines grow on the graph.
Ben decides to save more each week.
Drag Ben's handle to set his weekly savings. Make the two meet at week 15.
The crossing point has a name.
Where two lines cross is their intersection. Here it is (10, 70).
At that point both formulas are true: 20 + 5 × 10 = 70 and 50 + 2 × 10 = 70.
Finding the x that makes both true is solving the two equations together. A graph lets you read it off.
Make your own savings plan that meets Ana at week 5.
Pick a start and a weekly amount from the tiles. Your line is drawn with Ana's, and the meeting point glows.
Game: tie at the flag.
Runner A starts at 0. Runner B has a head start. Set B's speed so they reach the flag at the same moment.
A program can find the meeting week too.
This loop tries every week and prints the one where your plan and Ana's are equal. Step through it, or Run.
Make the lines meet at (4, 6).
The violet line is y = x + 2. The blue line starts at 10. Drag its handle.
A whole year of saving.
Drag time to week 52 and compare Ana, Ben and your plan. Then pick the plan you'd want.
Previous lesson: Reading Graphs Like Stories · Next lesson: Curves: When Growth Changes · Part of the course: Functions You Can See
Lessons are interactive and need JavaScript. Turn it on to play them.
