The number in front, and the lean
Draw y = x, y = 2x and y = 3x. What does the number in front do?
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Step 1 of 3
- The line through (0, 6) and (3, 12).
- Across 3 is the run. Up 6 is the rise.
- Slope = rise ÷ run = 6 ÷ 3 = 2.
The rule
The number in front of x tells the lean of the line. The lean is how steep it is, up or down. For example, y = 3x is steeper than y = x.
In y = ax + b, the number a is the slope. It is the change in y for one step in x. One step means x goes up by 1.
y = 2x + 6rises 2 for each step. The slope is 2.y = 5x + 6rises 5 for each step. That line is steeper thany = 2x + 6.y = 12 − 2xfalls 2 for each step. The slope is −2.
For y = 12 − 2x, write y = −2x + 12. The number in front of x is −2.
Rise is the change in y. Run is the change in x. Take any two points on the line. Rise ÷ run gives the same slope for every pair.
| Rule | Outputs at 0, 1, 2, 3 | Slope | Line does |
|---|---|---|---|
y = 2x + 6 | 6, 8, 10, 12 | 2 | rises |
y = 5x + 6 | 6, 11, 16, 21 | 5 | rises more |
y = 12 − 2x | 12, 10, 8, 6 | −2 | falls |
y = 12 − 5x | 12, 7, 2, −3 | −5 | falls more |
A positive slope means growth: the output rises. A negative slope means decay: the output falls.