Slope, Y-Intercept, and the Equation of a Line | The Learning ... - Free Printable

To find the slope from a table of values, we use the slope formula:

> Slope (m) = (change in y) / (change in x) = (y₂ - y₁) / (x₂ - x₁)

We can pick any two points from the table — as long as the relationship is linear (which all these tables are), the slope will be the same between any two points.

Let’s solve each one step by step.

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1. Table 1

| x | y |
|---|----|
| 0 | 5 |
| 1 | 10 |
| 2 | 15 |
| 3 | 20 |
| 4 | 25 |
| 5 | 30 |

Pick two points: (0, 5) and (1, 10)

→ m = (10 - 5) / (1 - 0) = 5 / 1 = 5

✔ Slope = 5

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2. Table 2

| x | y |
|----|----|
| -2 | 10 |
| -4 | 4 |
| -6 | -2 |
| -8 | -8 |
| -10| -14|
| -12| -20|

Pick (-2, 10) and (-4, 4)

→ m = (4 - 10) / (-4 - (-2)) = (-6) / (-2) = 3

✔ Slope = 3

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3. Table 3

| x | y |
|---|----|
| 1 | -5 |
| 3 | -2 |
| 5 | 1 |
| 7 | 4 |
| 9 | 7 |
|11 | 10 |

Pick (1, -5) and (3, -2)

→ m = (-2 - (-5)) / (3 - 1) = (3) / (2) = 1.5 or 3/2

✔ Slope = 3/2

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4. Table 4

| x | y |
|----|-----|
| -3 | -1 |
| -2 | -4 |
| -1 | -7 |
| 0 | -10 |
| 1 | -13 |
| 2 | -16 |

Pick (0, -10) and (1, -13)

→ m = (-13 - (-10)) / (1 - 0) = (-3)/1 = -3

✔ Slope = -3

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5. Table 5

| x | y |
|----|----|
| 3 | -6 |
| 0 | -2 |
| -3 | 2 |
| -6 | 6 |
| -9 | 10 |
| -12| 14 |

Pick (0, -2) and (3, -6)

→ m = (-6 - (-2)) / (3 - 0) = (-4)/3 = -4/3

✔ Slope = -4/3

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6. Table 6

| x | y |
|----|----|
| 0 | -3 |
| 4 | -2 |
| 8 | -1 |
|12 | 0 |
|16 | 1 |
|20 | 2 |

Pick (0, -3) and (4, -2)

→ m = (-2 - (-3)) / (4 - 0) = (1)/4 = 1/4

✔ Slope = 1/4

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7. Table 7

| x | y |
|---|---|
| 0 | 4 |
| 1 | 4 |
| 2 | 4 |
| 3 | 4 |
| 4 | 4 |
| 5 | 4 |

All y-values are the same → horizontal line!

→ m = (4 - 4)/(1 - 0) = 0/1 = 0

✔ Slope = 0

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8. Table 8

| x | y |
|----|----|
| -3 | 6 |
| -1 | 2 |
| 1 | -2 |
| 3 | -6 |
| 5 | -10|
| 7 | -14|

Pick (-3, 6) and (-1, 2)

→ m = (2 - 6) / (-1 - (-3)) = (-4)/(2) = -2

✔ Slope = -2

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## ✔ Final Answers:

1. 5
2. 3
3. 3/2
4. -3
5. -4/3
6. 1/4
7. 0
8. -2

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💡 Tip:

You can always check your answer by picking another pair of points — if you get the same slope, you’re correct! All these tables represent straight lines, so slope should be constant throughout.