To find the rate of change for each table, we calculate how much Y changes for every 1-unit increase in X. This is done by picking two points from the table and using the formula:
Rate of Change = (Change in Y) ÷ (Change in X)
= (Y₂ - Y₁) ÷ (X₂ - X₁)
We’ll do this for each table and verify with another pair of points to make sure it’s consistent.
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Table 1:
Points: (-8, -15) and (-3, 0)
Change in Y = 0 - (-15) = 15
Change in X = -3 - (-8) = 5
Rate = 15 ÷ 5 =
3
Check with another pair: (7, 30) and (8, 33)
Change in Y = 33 - 30 = 3
Change in X = 8 - 7 = 1
Rate = 3 ÷ 1 =
3 → Consistent.
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Table 2:
Points: (-10, -30) and (-8, -24)
Change in Y = -24 - (-30) = 6
Change in X = -8 - (-10) = 2
Rate = 6 ÷ 2 =
3
Check: (-2, -6) and (7, 21)
Change in Y = 21 - (-6) = 27
Change in X = 7 - (-2) = 9
Rate = 27 ÷ 9 =
3 → Consistent.
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Table 3:
Points: (-9, -66) and (-4, -31)
Change in Y = -31 - (-66) = 35
Change in X = -4 - (-9) = 5
Rate = 35 ÷ 5 =
7
Check: (0, -3) and (1, 4)
Change in Y = 4 - (-3) = 7
Change in X = 1 - 0 = 1
Rate = 7 ÷ 1 =
7 → Consistent.
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Table 4:
Points: (-5, 2) and (1, 8)
Change in Y = 8 - 2 = 6
Change in X = 1 - (-5) = 6
Rate = 6 ÷ 6 =
1
Check: (5, 12) and (10, 17)
Change in Y = 17 - 12 = 5
Change in X = 10 - 5 = 5
Rate = 5 ÷ 5 =
1 → Consistent.
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Table 5:
Points: (-5, -28) and (2, 7)
Change in Y = 7 - (-28) = 35
Change in X = 2 - (-5) = 7
Rate = 35 ÷ 7 =
5
Check: (6, 27) and (7, 32)
Change in Y = 32 - 27 = 5
Change in X = 7 - 6 = 1
Rate = 5 ÷ 1 =
5 → Consistent.
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Table 6:
Points: (-9, -13) and (-8, -12)
Change in Y = -12 - (-13) = 1
Change in X = -8 - (-9) = 1
Rate = 1 ÷ 1 =
1
Check: (-2, -6) and (6, 2)
Change in Y = 2 - (-6) = 8
Change in X = 6 - (-2) = 8
Rate = 8 ÷ 8 =
1 → Consistent.
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Table 7:
Points: (-5, -60) and (-1, -12)
Change in Y = -12 - (-60) = 48
Change in X = -1 - (-5) = 4
Rate = 48 ÷ 4 =
12
Check: (5, 60) and (7, 84)
Change in Y = 84 - 60 = 24
Change in X = 7 - 5 = 2
Rate = 24 ÷ 2 =
12 → Consistent.
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Table 8:
Points: (-6, -18) and (-4, -12)
Change in Y = -12 - (-18) = 6
Change in X = -4 - (-6) = 2
Rate = 6 ÷ 2 =
3
Check: (1, 3) and (5, 15)
Change in Y = 15 - 3 = 12
Change in X = 5 - 1 = 4
Rate = 12 ÷ 4 =
3 → Consistent.
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Table 9:
Points: (-6, -1) and (-5, 0)
Change in Y = 0 - (-1) = 1
Change in X = -5 - (-6) = 1
Rate = 1 ÷ 1 =
1
Check: (0, 5) and (10, 15)
Change in Y = 15 - 5 = 10
Change in X = 10 - 0 = 10
Rate = 10 ÷ 10 =
1 → Consistent.
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Table 10:
Points: (-5, -1) and (-4, 0)
Change in Y = 0 - (-1) = 1
Change in X = -4 - (-5) = 1
Rate = 1 ÷ 1 =
1
Check: (7, 11) and (10, 14)
Change in Y = 14 - 11 = 3
Change in X = 10 - 7 = 3
Rate = 3 ÷ 3 =
1 → Consistent.
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Table 11:
Points: (0, 0) and (1, 7)
Change in Y = 7 - 0 = 7
Change in X = 1 - 0 = 1
Rate = 7 ÷ 1 =
7
Check: (6, 42) and (8, 56)
Change in Y = 56 - 42 = 14
Change in X = 8 - 6 = 2
Rate = 14 ÷ 2 =
7 → Consistent.
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Table 12:
Points: (1, 13) and (6, 48)
Change in Y = 48 - 13 = 35
Change in X = 6 - 1 = 5
Rate = 35 ÷ 5 =
7
Check: (9, 69) and (10, 76)
Change in Y = 76 - 69 = 7
Change in X = 10 - 9 = 1
Rate = 7 ÷ 1 =
7 → Consistent.
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Final Answer:
1. 3
2. 3
3. 7
4. 1
5. 5
6. 1
7. 12
8. 3
9. 1
10. 1
11. 7
12. 7
Parent Tip: Review the logic above to help your child master the concept of constant rate of change worksheet with answers.
