MATEMATICA — Esercizio 03

📋 Testo

Comparing lines: draw the following three lines on the same graph and compare them:

• y = x
• y = 2x
• y = -x + 4

Observe and answer:
- Which line is steeper, y = x or y = 2x? Why?
- At what point do y = x and y = -x + 4 meet?
- What angle do y = x and y = -x + 4 form between them? What do you notice about their angular coefficients?

To add more functions, type each one in the field and click '+ Draw'.

Analisi: Guide the student to compare the angular coefficients: m = 1 (45°), m = 2 (steeper), m = -1 (descending). Ask: 'If m doubles, does the line become twice as steep?' Lead to the discovery that lines with m₁ · m₂ = -1 are perpendicular. For the intersection point, ask: 'How do you find where the lines cross without looking at the graph?'