Find the Intersection Point
Plot two lines and see where they meet to solve simultaneous equations.
Equation
y = -1*x + 4
Graph
Table
| x | y |
|---|---|
| -5 | 9 |
| -4 | 8 |
| -3 | 7 |
| -2 | 6 |
| -1 | 5 |
| 0 | 4 |
| 1 | 3 |
| 2 | 2 |
| 3 | 1 |
| 4 | 0 |
| 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 the line y = −x + 4. Rebuild the OTHER equation: y = x + 2 (slope 1, intercept 2).
- Your line must pass the meeting point of the two equations: check (1, 3) is on it.
- A different pair now, meeting at (2, 1). Rebuild the other equation y = 3x − 5: set its intercept to −5 first.
- Now slide the slope until your line passes through the meeting point (2, 1) — where two graphs cross is where both equations are true at once.
Check yourself
What does the intersection point of two lines represent in a system of equations?
If two lines are parallel, how many solutions does the system have?
- It is the only pair of (x, y) values that satisfies both equations simultaneously. — correct
- It is where the two lines have the same slope.
- It is the y-intercept of the steeper line.
- It is the average of the two x-intercepts.
- Zero solutions — correct
- One solution
- Infinite solutions
- Two solutions
Think about it
- If you increase the slope m1, does the line get steeper or flatter?