The Great Railway Mystery
Two parallel tracks never meet. Discover why some equations have no solution.
Equation
y = 1*x + 1
Graph
Table
| x | y |
|---|---|
| -3 | -2 |
| -2 | -1 |
| -1 | 0 |
| 0 | 1 |
| 1 | 2 |
| 2 | 3 |
| 3 | 4 |
What this lesson covers
What you do
You shape the function y = m1*x + c1 and watch the graph answer.
Challenges to clear
- Make the line parallel to y = 2x + 5: same slope 2, any DIFFERENT intercept.
- Now slide ONLY c1 anywhere you like — the tracks never meet. Slope must stay 2.
- A new pair of rails: make your line parallel to y = −3x + 4. Same slope −3, but a DIFFERENT intercept — identical lines would meet everywhere, not never.
- Now park the intercept at 7. Slope still −3, so the two lines run forever without touching: no solution.
Check yourself
Two trains leave stations on parallel tracks at the same speed. Will they ever meet?
If two lines are parallel, what is true about their slopes and y-intercepts?
- No, because parallel lines never intersect. — correct
- Yes, eventually, if the tracks are long enough.
- Only if they change their speed.
- Yes, at the origin (0,0).
- Same slope, different y-intercepts. — correct
- Different slopes, same y-intercepts.
- Same slope, same y-intercepts (they are the same line).
- Slopes are negative reciprocals.
Think about it
- If we change the slope (m1) to match the other line, what happens to the intersection point?