Grade 10 Proportional Equations Worksheet
This worksheet focuses on solving and understanding proportional equations for Grade 10 students, including direct and inverse variations.
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Standards
Topics
Proportional Equations: Grade 10
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Read each question carefully and solve for the unknown variable. Show all your work for full credit.
1. In a direct variation, as one quantity increases, the other quantity . The equation for direct variation is y = kx, where k is the .
2. In an inverse variation, as one quantity increases, the other quantity . The equation for inverse variation is y = k/x, where k is the .
3. Which of the following equations represents a direct variation?
y = 3x - 2
y = 5/x
y = 4x
y = x + 1
4. If y varies inversely as x, and y = 10 when x = 2, what is the constant of proportionality?
5
12
20
0.2
5. If y varies directly as x, and y = 15 when x = 3, find y when x = 7.
6. The amount of gas a car uses is directly proportional to the distance it travels. If a car uses 5 gallons of gas to travel 150 miles, how many gallons will it use to travel 240 miles?
7. The time it takes to complete a project varies inversely with the number of workers. If 4 workers can complete a project in 10 days, how many days will it take 8 workers to complete the same project?
8. The pressure (P) of a gas varies inversely with its volume (V). If P = 20 psi when V = 5 liters, find P when V = 4 liters.
9. If y = x/2, then y varies directly as x.
True
False
10. The graph of an inverse variation is a straight line passing through the origin.
True
False
11. Graph the direct variation equation y = 2x on the coordinate plane below.
12. Consider the inverse variation relationship where the product of x and y is 12 (xy = 12). Plot at least 4 points that satisfy this relationship in the first quadrant.
Match the description with the correct type of variation.
13. As x increases, y also increases proportionally.
a. Direct Variation
14. The product of x and y is constant.
b. Inverse Variation
15. Represented by y = k/x.
c. Neither
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