Unit Checkpoint
Demonstrate your mastery of proportional relationships.
Checkpoint Questions
Question 1: What is the constant of proportionality if y = 15 when x = 3?
Answer
k = y/x = 15/3 = 5. The equation is y = 5x.
Question 2: A car travels 180 miles on 6 gallons. What is the miles per gallon?
Answer
180/6 = 30 miles per gallon.
Question 3: Solve: 5/8 = x/24
Answer
Cross multiply: 5 x 24 = 8x. 120 = 8x. x = 15.
Question 4: Is the relationship y = 4x proportional? Explain.
Answer
Yes. It is in the form y = kx where k = 4, and it passes through the origin (0, 0).
Question 5: A graph shows a straight line through (0, 0) and (4, 12). What is k?
Answer
k = y/x = 12/4 = 3.
Question 6: If 4 notebooks cost $10, how much do 7 notebooks cost?
Answer
4/10 = 7/x. 4x = 70. x = $17.50.
Question 7: Table: x = 1, y = 4; x = 2, y = 8; x = 3, y = 12. Write the equation.
Answer
k = 4/1 = 8/2 = 12/3 = 4. Equation: y = 4x.
Question 8: On a map, 2 inches = 50 miles. How many inches represent 175 miles?
Answer
2/50 = x/175. 50x = 350. x = 7 inches.
Question 9: Is y = 3x + 2 proportional? Why or why not?
Answer
No. The +2 means when x = 0, y = 2, not 0. Proportional relationships must pass through the origin.
Question 10: If a 5-foot pole casts a 3-foot shadow, how long is the shadow of a 15-foot tree?
Answer
5/3 = 15/x. 5x = 45. x = 9 feet.
Self-Assessment
- 8-10 correct: Excellent! Ready to move on.
- 6-7 correct: Good! Review missed concepts.
- Below 6: Review lessons 1-5 before continuing.