Lesson 3 of 14
All the pairs make a line
Show on a big screenEvery 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.
Try the lab to finish this lesson.