Algebraic Connections Exploration

Name:

Date:

📊 Part 1: Forming and Connecting Equations

1. A mobile phone plan costs $25 per month plus $0.20 per text message. Which equation represents the total monthly cost (C) for sending t text messages?

C = 25t + 0.20

C = 25 + 0.20t

C = 0.20 + 25t

C = 25t × 0.20

2. A rectangle's length is 4 metres more than twice its width (w). The perimeter equation is:

P = 2w + 4

P = 6w + 8

P = 4w + 8

P = 2w + 8

3. When graphing y = 3x - 6, which features help you solve 3x - 6 = 0? (Check all that apply)

The y-intercept

The x-intercept

The slope

Where the line crosses the x-axis

4. Complete this statement: "Forming equations helps me _____________, graphing helps me _____________, and solving confirms my _____________."

🔗 Part 2: Digital Tool Exploration

5. Using GeoGebra or a graphing calculator, graph y = 2x + 3 and y = 2x - 1. What do you notice about these lines?

6. For the inequality 2x + 5 > 11:

a) Solve algebraically: x > _______

b) Using your digital tool, shade the region on the graph where y > 2x + 5 and y > 11. What does this show you about the solution?

7. A taxi charges $3.50 plus $2.20 per kilometre. You have $20 to spend.

a) Form an inequality: 3.50 + 2.20k _____ 20

b) Use your digital tool to graph this. What's the maximum distance you can travel? _______ km

c) Explain how the graph helped you find this answer:

💭 Part 3: Mathematical Reasoning

8. Explain in mathematical statements how you would solve 4x - 7 = 13. Use proper mathematical language.

9. A student says: "I can solve any linear equation just by looking at its graph." Do you agree? Explain your reasoning with an example.

10. Extension Challenge: Create your own real-world problem that connects forming, graphing, and solving. Include the equation, describe how graphing helps, and show the solution.