Slope-intercept form: y = mx + c
Move the m and c sliders. Watch the equation, graph, and table change together.
Equation
y = x
Graph
Table
| x | y |
|---|---|
| -3 | -3 |
| -2 | -2 |
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
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 the point (2, 5).
- Set the y-intercept to 4 — then (2, 5) forces the slope.
- Your slope is now ½: check the line is perpendicular to y = −2x + 1 (slopes multiply to −1).
- Start from the intercept: set c to 5, so the line crosses the y-axis at (0, 5).
- Now the slope, forced by one more point: the line must reach (3, −1). Down 6 over 3 across gives −2 — and that makes it perpendicular to y = 0.5x.
Check yourself
Which parameter controls how steep the line is?
What does the value of c tell you about the line?
Two lines are parallel exactly when…
- m — correct
- c
- neither
- both
- The slope
- Where the line crosses the y-axis (the y-intercept) — correct
- Where the line crosses the x-axis
- The angle the line makes with the x-axis
- they have the same y-intercept (c)
- they have the same slope (m) — correct
- they have the same equation
- they pass through the same point
Think about it
- Before you slide m, predict: what happens to the line when m grows? When m turns negative?
- Before you slide c, predict: which way will the line move when c grows?