Grade 10 Proportional Equations Worksheet

Proportional Equations: Grade 10

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?

4. If y varies inversely as x, and y = 10 when x = 2, what is the constant of proportionality?

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.

10. The graph of an inverse variation is a straight line passing through the origin.

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.