Let’s solve each problem step by step. We’re finding the slope (m) from a table using:
>
Slope formula:
> m = Δy / Δx = (change in y) / (change in x)
We pick any two points from the table, calculate how much y changes and how much x changes between them, then divide.
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Problem 1:
Points: (-3, 1), (0, 4), (-5, -1), etc.
Pick (-3, 1) and (0, 4):
Δy = 4 - 1 = 3
Δx = 0 - (-3) = 3
m = 3/3 =
1
Check with another pair: (-5, -1) and (-2, 2)
Δy = 2 - (-1) = 3
Δx = -2 - (-5) = 3
m = 3/3 = 1 → consistent!
✔ Slope = 1
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Problem 2:
Points: (-6, 27), (2, 3), (4, -3), etc.
Pick (-6, 27) and (2, 3):
Δy = 3 - 27 = -24
Δx = 2 - (-6) = 8
m = -24 / 8 =
-3
Check with (4, -3) and (9, -18):
Δy = -18 - (-3) = -15
Δx = 9 - 4 = 5
m = -15 / 5 = -3 → consistent!
✔ Slope = -3
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Problem 3:
Points: (5, 27), (0, -8), (9, 55), etc.
Pick (5, 27) and (0, -8):
Δy = -8 - 27 = -35
Δx = 0 - 5 = -5
m = -35 / -5 =
7
Check with (9, 55) and (4, 20):
Δy = 20 - 55 = -35
Δx = 4 - 9 = -5
m = -35 / -5 = 7 → consistent!
✔ Slope = 7
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Problem 4:
Points: (1, 0), (-7, -24), (-5, -18), etc.
Pick (1, 0) and (-7, -24):
Δy = -24 - 0 = -24
Δx = -7 - 1 = -8
m = -24 / -8 =
3
Check with (-5, -18) and (-9, -30):
Δy = -30 - (-18) = -12
Δx = -9 - (-5) = -4
m = -12 / -4 = 3 → consistent!
✔ Slope = 3
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Problem 5:
Points: (-3, 20), (-5, 32), (-4, 26), etc.
Pick (-3, 20) and (-5, 32):
Δy = 32 - 20 = 12
Δx = -5 - (-3) = -2
m = 12 / -2 =
-6
Check with (-2, 14) and (8, -46):
Δy = -46 - 14 = -60
Δx = 8 - (-2) = 10
m = -60 / 10 = -6 → consistent!
✔ Slope = -6
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Problem 6:
Points: (5, -4), (0, -9), (-7, -16), etc.
Pick (5, -4) and (0, -9):
Δy = -9 - (-4) = -5
Δx = 0 - 5 = -5
m = -5 / -5 =
1
Check with (-5, -14) and (-3, -12):
Δy = -12 - (-14) = 2
Δx = -3 - (-5) = 2
m = 2 / 2 = 1 → consistent!
✔ Slope = 1
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Problem 7:
Points: (-6, -2), (-1, -4.5), (4, -7), etc.
Pick (-6, -2) and (-1, -4.5):
Δy = -4.5 - (-2) = -2.5
Δx = -1 - (-6) = 5
m = -2.5 / 5 =
-0.5
Check with (4, -7) and (7, -8.5):
Δy = -8.5 - (-7) = -1.5
Δx = 7 - 4 = 3
m = -1.5 / 3 = -0.5 → consistent!
✔ Slope = -0.5
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Problem 8:
Points: (-7, -2), (6, 11), (-5, 0), etc.
Pick (-7, -2) and (6, 11):
Δy = 11 - (-2) = 13
Δx = 6 - (-7) = 13
m = 13 / 13 =
1
Check with (-5, 0) and (9, 14):
Δy = 14 - 0 = 14
Δx = 9 - (-5) = 14
m = 14 / 14 = 1 → consistent!
✔ Slope = 1
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Problem 9:
Points: (-2, -6.5), (4, -8), (7, -8.75), etc.
Pick (-2, -6.5) and (4, -8):
Δy = -8 - (-6.5) = -1.5
Δx = 4 - (-2) = 6
m = -1.5 / 6 =
-0.25
Check with (7, -8.75) and (-8, -5):
Δy = -5 - (-8.75) = 3.75
Δx = -8 - 7 = -15
m = 3.75 / -15 = -0.25 → consistent!
✔ Slope = -0.25
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Final Answer:
1. 1
2. -3
3. 7
4. 3
5. -6
6. 1
7. -0.5
8. 1
9. -0.25
Parent Tip: Review the logic above to help your child master the concept of finding slope from a table worksheet.
