The Slope and Intercept Dance
Discover how m tilts the line and c lifts it up in y = m*x + c
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 the line pass through (3, 5).
- Make the line pass through (-3, -1) AND (1, 3) at the same time.
- Your own line now. Fix the intercept first: make it cross the y-axis at (0, −4). The slope can be anything for the moment.
- Now set the slope so it also passes (2, 2) — two conditions, two sliders, one line.
Check yourself
In y = m*x + c, if m is negative, what happens to the line as x increases?
Which parameter determines where the line crosses the y-axis?
If a line passes through (0, 4), what is the value of c?
- The line goes up (positive slope)
- The line goes down (negative slope) — correct
- The line stays horizontal
- The line becomes vertical
- m (the slope)
- c (the y-intercept) — correct
- x (the input)
- y (the output)
- 0
- 4 — correct
- 1
- Cannot be determined
Think about it
- If you increase m, does the line get steeper or flatter?
- If you increase c, does the line move up or down?