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Proportional and Linear Relationships
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Proportional and Linear Relationships
📊 Part 1: Identifying Relationships
1. A proportional relationship is a straight line that passes through the point (_____, _____).
2. Which of the following equations represents a proportional relationship?
y = 3x + 2
y = 5x
y = -2x + 7
y = x - 4
3. The unit rate in a proportional relationship is represented by the _____________ of the line.
4. Check all that represent functions:
A mapping where each input has exactly one output
A vertical line on a graph
A table where x = 2 appears twice with different y-values
The equation y = 4x - 1
📈 Part 2: Analyzing Data and Graphs
5. A line passes through points (0, 0) and (3, 12). What is the unit rate?
6. Is the relationship y = 2x + 5 proportional or non-proportional? Explain your reasoning.
7. In direct variation, if y = kx and y = 15 when x = 3, find the value of k.
k = _______
8. Look at this table. Is this relationship proportional? Circle your answer and explain.
YES or NO
x: 2, 4, 6, 8
y: 6, 12, 18, 24
🎯 Part 3: Systems of Equations
9. Solve this system of equations by finding where the lines intersect:
y = 2x + 1
y = -x + 7
Solution: x = _______, y = _______
10. A pizza costs $8 plus $2 per topping (y = 2x + 8). A sandwich costs $12 plus $1 per topping (y = x + 12). How many toppings would make both items cost the same?
Number of toppings: _______
Cost of each item: $_______
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