All the pairs make a line
Every pair that fits the equation is a point on a line. Slide along it.
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Step 1 of 4
- A numbered grid. Each mark is 1 unit.
- Plot (0, 4), (3, 2) and (6, 0).
- One straight line passes through all three.
- Every other point of that line makes both sides equal too.
The rule
A pair satisfies an equation when it makes both sides equal.
Rule: Every pair that satisfies the equation lands on one straight line. Every point of that line satisfies the equation too.
Take 2x + 3y = 12. Pick x. The equation then gives y.
| x | 2x + 3y = 12 | y | Pair |
|---|---|---|---|
| 0 | 0 + 3y = 12 | 4 | (0, 4) |
| 3 | 6 + 3y = 12 | 2 | (3, 2) |
| 6 | 12 + 3y = 12 | 0 | (6, 0) |
An axis is a number line on the grid. The x-axis runs across. The y-axis runs up.
Where a line meets an axis has a name: the intercept. This line meets the y-axis at (0, 4). It meets the x-axis at (6, 0). Both are easy to find. Set one letter to 0. The equation gives you the other.
The line is the equation, drawn.