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Proportional Relationships Practice
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Proportional Relationships Practice
Compare y ÷ x for each pair. A proportional relationship has the same unit rate for every pair and includes (0, 0). Show your calculations and explain your reasoning.
Check the tables
1.The table has x-values 3, 6, and 9, and corresponding y-values 7.5, 15, and 22.5. Is y proportional to x? Find y ÷ x for each pair and explain.
2.For the pairs (2, 5), (4, 11), and (6, 17), calculate y ÷ x for each pair. Does the table represent a proportional relationship? Explain.
3.A smoothie recipe uses 2 cups of yogurt for every 5 cups of fruit. If x is cups of fruit and y is cups of yogurt, which equation represents the relationship?
- y = 2.5x
- y = 0.4x
- y = x + 3
- y = 5x
Find the rate and equation
4.A machine fills 18 bottles in 3 minutes. If x is the number of minutes and y is the number of bottles filled at a constant rate, find the constant of proportionality and write an equation for y.
5.For the equation y = 3.25x, what is the constant of proportionality, and what is y when x = 8?
Connect situations, equations, and graphs
6.Match each situation to its equation. Then name the proportional situations.
- A. A bike rental costs $7 for each hour, h; total cost is c.
- B. A delivery costs $4 plus $2 for each mile, m; total cost is d.
- C. A printer makes 12 pages each minute, t; total pages are p.
- D. A plant is 5 inches tall at the start and grows 3 inches each week, w; its height is H.
- d = 2m + 4
- H = 3w + 5
- p = 12t
- c = 7h
7.A graph plots the points (0, 0), (2, 5), (4, 10), and (6, 15) on a straight line. Is the relationship proportional? State the unit rate.
8.A straight-line graph passes through (0, 4), (2, 8), and (4, 12). Is the relationship proportional? Explain using the graph's intercept.
9.A proportional relationship has the equation y = 4.5x. What point on its graph corresponds to x = 6?
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