Every pair is a point
Plot y = 3x + 2 on a grid. Where does each pair of input and output go?
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Step 1 of 3
- A grid. Inputs go across. Outputs go up.
- Plot (0, 2), (1, 5), (2, 8) and (3, 11).
- One straight line passes through all four.
The rule
Each pair is one point: x across, then y up.
An input x and its output y make a pair (x, y). The input comes first.
Take y = 3x + 2.
Input x | Working | Output y | Pair |
|---|---|---|---|
| 0 | 3 × 0 + 2 | 2 | (0, 2) |
| 1 | 3 × 1 + 2 | 5 | (1, 5) |
| 2 | 3 × 2 + 2 | 8 | (2, 8) |
| 3 | 3 × 3 + 2 | 11 | (3, 11) |
The four points lie on one straight line. The graph of a rule of degree 1 is a straight line.
If a point is on the line, its pair fits the rule. Test (7, 23): 3 × 7 + 2 = 21 + 2 = 23. The pair fits.
y = x² is different. Its pairs are (0, 0), (1, 1), (2, 4), (3, 9). The gaps between outputs are 1, 3, 5. They are not equal. So these points do not lie on one line.