Lesson 4 of 14
Two lines and one shared spot
Show on a big screenDraw both equations on one grid. Where do the two lines cross? Tap the crossing.
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Step 1 of 4
- A grid, ready for both claims.
- Line 1:
2x + 3y = 12, through (0, 4) and (6, 0). - Line 2:
x − y = 1, through (1, 0) and (0, −1). - They cross at (3, 2), the solution of the pair.
The rule
The lines cross at (3, 2).
Rule: A solution is a point on both lines at once. It is the crossing.
Each line is drawn from its own equation. The crossing shows only when both lines are on the same grid.
In the table, level means both sides are equal.
| Equation | At (3, 2) | Claim says | Level? |
|---|---|---|---|
2x + 3y = 12 | 2·3 + 3·2 = 12 | 12 | yes |
x − y = 1 | 3 − 2 = 1 | 1 | yes |
A line's lean is how steeply it slopes up or down. Two lines that lean differently share exactly one point. Line 1 falls 2 for every 3 steps right. Line 2 rises 1 for every 1 step right. Different leans mean one crossing.
A point read between grid marks is only an estimate. Algebra finds the exact pair.
Try the lab to finish this lesson.