The number on its own
Three lines have the same slope. Where does each cut the y-axis, the up-and-down number line?
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y = 2x, y = 2x + 5, y = 2x + 9. Step 1 of 3
- Three lines with the same slope:
y = 2x,y = 2x + 5,y = 2x + 9. - They cut the y-axis at 0, 5 and 9.
- The same slope, at different heights. They never meet.
The rule
The number with no x tells where a line cuts the y-axis. For these lines, it is 0, 5 and 9.
Every point on the y-axis has x = 0. At x = 0, the term ax is 0. So y = b. The line cuts the y-axis at (0, b).
The number b is the y-intercept.
y = 3x − 2cuts the y-axis at (0, −2).y = 2x + 5cuts it at (0, 5).
| Rule | y-intercept | Outputs at 1, 2, 3 | Slope |
|---|---|---|---|
y = 2x | 0 | 2, 4, 6 | 2 |
y = 2x + 5 | 5 | 7, 9, 11 | 2 |
y = 2x + 9 | 9 | 11, 13, 15 | 2 |
y = 5x + 9 | 9 | 14, 19, 24 | 5 |
Lines with the same slope and different b are parallel. Parallel lines never meet.
To read a drawn line, find where the line cuts the y-axis. That height is b. Then measure rise ÷ run between two points. That number is a.