MATEMATICA — Esercizio 04

📋 Testo

Parallel and perpendicular lines: draw the following lines and study the relationships between them:

• y = 0.5x + 1
• y = 0.5x - 2
• y = -2x + 3

Answer the questions:
- Do the first two lines meet? Why or why not?
- What is the vertical distance between y = 0.5x + 1 and y = 0.5x - 2?
- Is the third line perpendicular to the first two? How do you verify it with the angular coefficients?
- Find the intersection point between y = 0.5x + 1 and y = -2x + 3.

Hint: two lines are parallel if they have the same m, perpendicular if m₁ · m₂ = -1.

Analisi: Introduce the concept of parallelism (same m, different q) and perpendicularity (m₁ · m₂ = -1). Ask: 'Looking at the graph, do the first two lines seem to approach each other? Will they ever meet?' For the intersection, guide toward solving the linear system. Ask: 'If two parallel lines have the same slope but different intercept, what changes in their equation?'