The Meeting Point
Find the solution to two equations by seeing where their lines cross.
Equation
y = -1*x + 6
Graph
Table
| x | y |
|---|---|
| -5 | 11 |
| -4 | 10 |
| -3 | 9 |
| -2 | 8 |
| -1 | 7 |
| 0 | 6 |
| 1 | 5 |
| 2 | 4 |
| 3 | 3 |
| 4 | 2 |
| 5 | 1 |
What this lesson covers
What you do
You shape the function y = m1*x + c1 and watch the graph answer.
Challenges to clear
- You start as y = −x + 6. Rebuild the FIRST equation: y = x + 2.
- Your line passes the meeting point of the pair: check (2, 4) is on it.
- A different pair meets at (3, 1). Rebuild the first equation y = −2x + 7 — set its intercept to 7 first.
- Now slide the slope until the line passes the meeting point (3, 1). Where the two graphs cross IS the solution of the pair.
Check yourself
What does the point where two lines cross tell us about the simultaneous equations?
If two lines never cross, what does that mean for the equations?
- It is the only pair of (x, y) values that satisfies both equations at the same time. — correct
- It shows the sum of the two y-intercepts.
- It is the average of the two slopes.
- It indicates where the lines are parallel.
- There is no solution because the lines are parallel. — correct
- There are infinite solutions because they are the same line.
- The solution is at infinity.
- The equations cannot be solved graphically.
Think about it
- Imagine the second line y = −x + 6 on this graph. Where does it cross y = x + 2?