Math worksheet for finding slope from a table of values, including examples and step-by-step instructions.

Let’s solve each table step by step to find the slope (m) using the formula:

> m = Δy / Δx = (y₂ - y₁) / (x₂ - x₁)

We’ll pick any two points from each table — it doesn’t matter which, as long as they’re in order. We’ll use the first and last row for consistency.

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🔹 Table 1:

| x | y |
|----|----|
| 5 | 10 |
| 8 | 8 |
| 11 | 6 |
| 14 | 4 |

Pick point 1: (5, 10)
Pick point 2: (14, 4)

Δy = y₂ - y₁ = 4 - 10 = -6
Δx = x₂ - x₁ = 14 - 5 = 9

So, m = Δy / Δx = -6 / 9 → simplify → -2/3

✔ Check with another pair: (8,8) and (11,6)
Δy = 6 - 8 = -2
Δx = 11 - 8 = 3
m = -2/3 → same! Good.

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🔹 Table 2:

| x | y |
|----|----|
| -2 | 5 |
| 0 | 10 |
| 2 | 15 |
| 4 | 20 |

Pick (-2, 5) and (4, 20)

Δy = 20 - 5 = 15
Δx = 4 - (-2) = 4 + 2 = 6

m = 15 / 6 → simplify → divide numerator and denominator by 3 → 5/2

✔ Check with (0,10) and (2,15):
Δy = 15 - 10 = 5
Δx = 2 - 0 = 2
m = 5/2 → same!

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🔹 Table 3:

| x | y |
|----|----|
| 3 | 20 |
| 6 | 16 |
| 12 | 8 |
| 15 | 4 |

Pick (3,20) and (15,4)

Δy = 4 - 20 = -16
Δx = 15 - 3 = 12

m = -16 / 12 → simplify → divide by 4 → -4/3

✔ Check with (6,16) and (12,8):
Δy = 8 - 16 = -8
Δx = 12 - 6 = 6
m = -8/6 = -4/3 → same!

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🔹 Table 4:

| x | -1 | 0 | 1 | 2 |
|----|----|---|---|---|
| y | 0 | 2 | 4 | 6 |

Pick (-1, 0) and (2, 6)

Δy = 6 - 0 = 6
Δx = 2 - (-1) = 2 + 1 = 3

m = 6 / 3 = 2

✔ Check with (0,2) and (1,4):
Δy = 4 - 2 = 2
Δx = 1 - 0 = 1
m = 2/1 = 2 → same!

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Final Answer:

Table 1:
Δy = -6, Δx = 9, m = -2/3

Table 2:
Δy = 15, Δx = 6, m = 5/2

Table 3:
Δy = -16, Δx = 12, m = -4/3

Table 4:
Δy = 6, Δx = 3, m = 2