Two changing quantities: tables, graphs, equations

Answer Key - Grade 6 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Table. m (minutes): 1, 2, 3. l (liters): 4, 8, 12. Esme's bucket gets 4 more liters each minute. Each row is m equal bars of the same size. What equation for l fits?

   l = 4m
2. 2.

   Table. m (minutes): 3, 6, 9. l (liters): 18, 36, 54. Pia's garden hose runs at a steady rate. Each row is m equal bars of the same size. What equation for l fits?

   l = 6m
3. 3.

   Table. t (hours): 1, 2, 3. d (miles): 5, 10, 15. Ren jogs at a steady speed. Each row is t equal bars of the same size. What is d when t is 4?

   20
4. 4.

   Table. w (weeks): 1, 2, 3. h (centimeters): 7, 8, 9. Esme measures a seedling each week. In every row, h is a bar for w with one extra piece added on. What equation for h fits?

   h = w + 6
5. 5.

   Table. s (Esme's blocks): 5, 6, 7. a (Ari's blocks): 1, 2, 3. Ari and Esme each build a tower of blocks. In every row, s is a bar for a with one extra piece added on. What equation for s fits?

   s = a + 4
6. 6.

   Table. b (Bo's acorns): 1, 2, 3. k (Kira's acorns): 12, 13, 14. Bo and Kira collect acorns in the park. In every row, k is a bar for b with one extra piece added on. What equation for k fits?

   k = b + 11
7. 7.

   Table. d (miles): 35, 70, 105. t (hours): 1, 2, 3. Jun rides a bus at a steady speed. The table shows miles d and hours t. Which is the independent variable? (The independent variable is the one we choose. The other one depends on it.)

   • Both: neither one depends on the other
   • t (hours)
   • d (miles)
8. 8.

   Table. p (pages): 15, 30, 45. h (hours): 1, 2, 3. Luz reads at a steady speed. The table shows pages p and hours h. Which is the independent variable? (The independent variable is the one we choose. The other one depends on it.)

   • h (hours)
   • Both: neither one depends on the other
   • p (pages)
9. 9.

   Milo's run is graphed. Miles d are on the vertical axis and hours t are on the horizontal axis. What does the plotted point say? (A point is written (across, up).)

   • t = 4 and d = 20
   • d = 20 for each hour
   • t = 20 and d = 4
10. 10.

    Pia's bucket filling is graphed. Liters l are on the vertical axis and minutes m are on the horizontal axis. What does the plotted point say? (A point is written (across, up).)

    • l = 15 for each minute
    • m = 15 and l = 3
    • m = 3 and l = 15