The Intersection Point
Find where two lines meet to solve simultaneous equations graphically.
Equation
y = x
Graph
Table
| x | y |
|---|---|
| -5 | -5 |
| -4 | -4 |
| -3 | -3 |
| -2 | -2 |
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
What this lesson covers
What you do
You shape the function y = m*x + c and watch the graph answer.
Challenges to clear
- Make your line pass through the point (2, 4).
- Make your line pass through (0, 0) and have a slope of 2.
- Build a different line: start it at (0, 3) on the y-axis.
- Now make it fall through (4, −1) too — a downhill slope, so m goes negative.
Check yourself
Two lines intersect at a single point (2, 4). What does this point represent for the system of equations?
- The x-coordinate is the solution for y.
- It is the only pair of (x, y) values that satisfies both equations simultaneously. — correct
- It shows where the lines are parallel.
- It is the average of the two y-intercepts.
Think about it
- If you increase the slope 'm', does the line get steeper or flatter?
- If you increase the intercept 'c', which way does the line move?