Read a graph as a story: rising, falling, steady

Grade 8 Math Worksheet

Circle the best answer.

1. 1.

   Ari watches a tank drain. The graph shows liters left against minutes. What are the rate of change and the initial value, and what does each mean?

   • The rate is 5 liters each minute, so the tank gains 5 liters a minute; it started with 44 liters.
   • The rate is 44 liters each minute, so the tank loses 44 liters a minute; it started with 5 liters.
   • The rate is −5 liters each minute, so the tank loses 5 liters a minute; it started with 34 liters.
   • The rate is −5 liters each minute, so the tank loses 5 liters a minute; it started with 44 liters.
2. 2.

   Bo measures a growing plant. The graph shows centimeters tall against days. What are the rate of change and the initial value, and what does each mean?

   • The rate is −4 centimeters each day, so the plant shrinks 4 centimeters a day; it started 7 centimeters tall.
   • The rate is 7 centimeters each day, so the plant grows 7 centimeters a day; it started 4 centimeters tall.
   • The rate is 4 centimeters each day, so the plant grows 4 centimeters a day; it started 19 centimeters tall.
   • The rate is 4 centimeters each day, so the plant grows 4 centimeters a day; it started 7 centimeters tall.
3. 3.

   Esme tracks a candle getting shorter. The graph shows millimeters tall against minutes. What are the rate of change and the initial value, and what does each mean?

   • The rate is −2 millimeters each minute, so the candle shrinks 2 millimeters a minute; it started 26 millimeters tall.
   • The rate is −2 millimeters each minute, so the candle shrinks 2 millimeters a minute; it started 30 millimeters tall.
   • The rate is 2 millimeters each minute, so the candle grows 2 millimeters a minute; it started 30 millimeters tall.
   • The rate is 30 millimeters each minute, so the candle shrinks 30 millimeters a minute; it started 2 millimeters tall.
4. 4.

   Jun tracks a savings jar. The graph shows dollars saved against weeks. What are the rate of change and the initial value, and what does each mean?

   • The rate is 22 dollars each week, so savings grow 22 dollars a week; it started with 3 dollars.
   • The rate is 3 dollars each week, so savings grow 3 dollars a week; it started with 22 dollars.
   • The rate is −3 dollars each week, so savings shrink 3 dollars a week; it started with 10 dollars.
   • The rate is 3 dollars each week, so savings grow 3 dollars a week; it started with 10 dollars.
5. 5.

   Luz studies a graph of distance biked against time. Is the function linear, and why?

   • Not linear: the rate is 2 from A to B, 4 from B to C and 8 from C to D.
   • Linear: it starts at the origin, so it is a straight line.
   • Linear: the graph rises from left to right.
   • Linear: the first and last corners fit a line with rate 4.
6. 6.

   Milo studies a graph of savings in a jar against time. Is the function linear, and why?

   • Not linear: the piece from C to D is longer than the piece from A to B.
   • Not linear: the line bends at B and at C.
   • Linear: each piece rises 2 for each 1 across, so the corners sit on one line.
   • Not linear: it starts at 9, not at 0.
7. 7.

   Noah studies a graph of water in a cup against time. Is the function linear, and why?

   • Linear: the first and last corners fit a line with rate 3.
   • Not linear: the rate is 1 from A to B, 3 from B to C and 4 from C to D.
   • Linear: the amount grows the whole time.
   • Linear: it begins at (0, 0), so it is a line.
8. 8.

   Ren compares two plants. B's graph is shown. A's table (x | y) is 1 | 15, 3 | 21, 5 | 27. Which statement is right about rates and initial values?

   • B has the greater rate of change, 5 against 3, but A has the greater initial value, 12 against 7.
   • A has both the greater rate, 6 against 5, and the greater initial value, 12 against 7.
   • A has the greater rate, 12 against 7, but B has the greater initial value, 5 against 3.
   • B has both the greater rate, 5 against 3, and the greater initial value, because its first value, 17, is more than 15.
9. 9.

   Tala compares two savings jars. A's graph is shown. B's table (x | y) is 2 | 14, 5 | 20, 8 | 26. Which statement is right about rates and initial values?

   • B has both the greater rate, 6 against 4, and the greater initial value, 10 against 5.
   • A has the greater rate of change, 4 against 2, but B has the greater initial value, 10 against 5.
   • A has both the greater rate, 4 against 2, and the greater initial value, because its first value, 17, is more than 14.
   • B has the greater rate, 10 against 5, but A has the greater initial value, 4 against 2.
10. 10.

    Zee compares two tubs. B's graph is shown. A's table (x | y) is 1 | 13, 3 | 21, 5 | 29. Which statement is right about rates and initial values?

    • B has both the greater rate, 6 against 4, and the greater initial value, because its first value, 14, is more than 13.
    • A has the greater rate, 9 against 2, but B has the greater initial value, 6 against 4.
    • B has the greater rate of change, 6 against 4, but A has the greater initial value, 9 against 2.
    • A has both the greater rate, 8 against 6, and the greater initial value, 9 against 2.