📊 Part 1: Understanding Linear Equations

1. For the equation y = 3x + 2, what is the slope (m) and y-intercept (b)?

Slope = 2, Y-intercept = 3

Slope = 3, Y-intercept = 2

Slope = 5, Y-intercept = 0

Slope = 1, Y-intercept = 5

2. A taxi charges $3.50 for the initial ride plus $2.25 per mile. Which equation represents this situation?

y = 3.50x + 2.25

y = 2.25x + 3.50

y = 5.75x

y = x + 5.75

3. What happens to a line when the slope (m) is negative?

The line goes up from left to right

The line goes down from left to right

The line is horizontal

The line is vertical

4. Complete the table for the equation y = -2x + 5:

x	0	1	2	3
y	____	____	____	____

✏️ Part 2: Verbal Descriptions and Analysis

5. Write a verbal description for the equation y = 4x - 3. Explain what the slope and y-intercept mean in real-world terms.

6. A gym membership costs $25 per month plus a one-time enrollment fee of $50. Write the linear equation that represents the total cost (y) after x months.

Equation: y = ________________

7. Compare these two equations and explain how their graphs would be different:

Equation A: y = 2x + 1

Equation B: y = 2x + 4

8. Predict what happens to the graph when you change the slope from m = 1 to m = 3 (keeping the same y-intercept). Explain your reasoning.

🔍 Part 3: Critical Thinking

9. A phone plan charges $30 per month plus $0.10 for each text message over 500. If someone sends 750 text messages in a month, what would their total bill be? Show your work.

10. Create your own real-world scenario that can be modeled with a linear equation in the form y = mx + b. Write the scenario, identify the slope and y-intercept, and write the equation.