📊 Part 1: Identifying Proportional Relationships

1. Which equation represents a proportional relationship?

y = 3x + 2

y = 5x

y = x - 4

y = 2x + 1

2. A proportional relationship graph MUST pass through which point?

(1, 1)

(0, 0)

(1, 0)

(0, 1)

3. If 4 gallons of gas cost $12, what is the unit rate (cost per gallon)?

Unit rate: $_______ per gallon

Write the proportional equation: y = _______

4. Check ALL the characteristics of proportional relationships:

The graph passes through the origin

The ratio y/x is constant

The equation is in the form y = kx

The y-intercept is always zero

🎯 Part 2: Functions and Linear Relationships

5. Look at this table. Is this relationship proportional? Circle: YES or NO

Table: (1, 3), (2, 6), (3, 9), (4, 12)

Explain your reasoning:

6. Which of the following represents a function?

{(1, 2), (1, 3), (2, 4)}

{(1, 2), (2, 3), (3, 4)}

{(1, 2), (2, 2), (1, 4)}

{(1, 3), (1, 5), (2, 6)}

7. Complete the statement: A relationship is a function if every input has exactly _______ output.

8. The equation y = 4x represents direct variation. What is the constant of variation?

Constant of variation: k = _______

🔍 Part 3: Problem Solving

9. Maria earns $15 per hour babysitting. Write an equation for her total earnings.

Let h = hours worked and E = total earnings

Equation: E = _______

Is this proportional? Circle: YES or NO

10. A taxi charges $3 plus $2 per mile. Write an equation for the total cost.

Let m = miles and C = total cost

Equation: C = _______

Is this proportional? Circle: YES or NO

Explain why or why not:

11. Create your own example of a proportional relationship from real life:

Proportional Linear Relationships

Proportional Linear Relationships

📊 Part 1: Identifying Proportional Relationships

🎯 Part 2: Functions and Linear Relationships

🔍 Part 3: Problem Solving

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