M4.8.7 For the adult
Two equations on a graph
The lines y = x + 1 and y = 7 − x cross at (3, 4). What does that point tell me?
What this chapter teaches
Each equation in x and y is a straight line. Where two lines cross, one pair of numbers fits both equations. Parallel lines never cross, so there is no solution, and two equations for the same line have infinitely many.
Three questions to ask
There is no one right wording. Listen for the idea.
- What does the point where two lines cross tell you about the two equations?
- Why do two lines with the same gradient and different c have no solution?
- Why is algebra more exact than reading a graph?
After the chapter, the learner can
- Solve two equations by finding where their lines cross
- Explain why parallel lines give no answer
What they copy into their notebook
The crossing point of two lines is the solution. Parallel lines: no solution. The same line: infinitely many. A graph estimates, algebra is exact.