Lesson 4-4: Direct Variation — Practice Questions

1. 1. Which statement best describes the graph of a direct variation?

   • A. The graph is a straight line.
   • B. The graph is a curve passing through the origin.
   • C. The graph is a straight line passing through the origin.
   • D. The graph does not need to pass through the origin.

2. 2. The equation for a line is `C = 4h + 5`. To determine if it shows direct variation, we check if it passes through the origin. When `h=0`, the value of `C` is ___.

3. 3. Which of the following equations represents a direct variation?

   • A. $`y = x^2`$
   • B. `y = 6x`
   • C. `y = 3x + 2`
   • D. `y = 8`

4. 4. Why does the equation `d = 5t - 1` NOT represent a direct variation?

   • A. Its graph is a curve.
   • B. It has a negative term.
   • C. Its graph does not pass through the origin.
   • D. Its graph is a vertical line.

5. 5. For a relationship to be a direct variation, its graph must be a straight line that passes through the point `(0, ___)`.

6. 6. A recipe for lemonade calls for 3 lemons to make 5 glasses. How many lemons are needed to make 20 glasses of lemonade? ___ lemons.

7. 7. A car can travel 120 miles on 4 gallons of gasoline. At this rate, how many gallons are needed to travel 300 miles? ___ gallons.

8. 8. A factory machine produces 90 toys in 3 hours. Which proportion correctly finds the number of toys, $t$, the machine can produce in 8 hours?

   • A. $\frac{90}{3} = \frac{t}{8}$
   • B. $\frac{90}{3} = \frac{8}{t}$
   • C. $\frac{3}{90} = \frac{t}{8}$
   • D. $\frac{90}{t} = \frac{8}{3}$

9. 9. If 4 pounds of potatoes cost 6.00 dollars, what is the cost of 10 pounds of potatoes? ___ dollars.

10. 10. An employee earns 112 dollars for working 8 hours. If the pay rate is constant, how much will the employee earn for working 5 hours? ___ dollars.