Finding Slope - Free Printable

Let's solve each table to find the slope ($ m $) of the line represented by the data. The slope is calculated using the formula:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

We can pick any two points from each table to compute the slope. Let’s go through each one.

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①

| x | y |
|---|---|
| -6 | 8 |
| -2 | 4 |
| 2 | 0 |
| 6 | -4 |
| 10 | -8 |

Let’s use the first two points: $(-6, 8)$ and $(-2, 4)$

$$
m = \frac{4 - 8}{-2 - (-6)} = \frac{-4}{4} = -1
$$

Check with another pair: (2, 0) and (6, -4)

$$
m = \frac{-4 - 0}{6 - 2} = \frac{-4}{4} = -1
$$

✔ Consistent. So, $ m = -1 $

---

②

| x | y |
|---|---|
| 3 | -1 |
| 4 | -3 |
| 5 | -5 |
| 6 | -7 |
| 7 | -9 |

Use (3, -1) and (4, -3):

$$
m = \frac{-3 - (-1)}{4 - 3} = \frac{-2}{1} = -2
$$

Check with (5, -5) and (6, -7):

$$
m = \frac{-7 - (-5)}{6 - 5} = \frac{-2}{1} = -2
$$

✔ Consistent. So, $ m = -2 $

---

③

| x | y |
|---|---|
| -1 | -10 |
| 0 | -5 |
| 1 | 0 |
| 2 | 5 |
| 3 | 10 |

Use (-1, -10) and (0, -5):

$$
m = \frac{-5 - (-10)}{0 - (-1)} = \frac{5}{1} = 5
$$

Check (1, 0) and (2, 5):

$$
m = \frac{5 - 0}{2 - 1} = \frac{5}{1} = 5
$$

✔ Consistent. So, $ m = 5 $

---

④

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

Use (-4, 2) and (-2, 1):

$$
m = \frac{1 - 2}{-2 - (-4)} = \frac{-1}{2} = -\frac{1}{2}
$$

Check (0, 0) and (2, -1):

$$
m = \frac{-1 - 0}{2 - 0} = \frac{-1}{2} = -\frac{1}{2}
$$

✔ Consistent. So, $ m = -\frac{1}{2} $

---

⑤

| x | y |
|---|---|
| -9 | 10 |
| -3 | 8 |
| 3 | 6 |
| 9 | 4 |
| 15 | 2 |

Use (-9, 10) and (-3, 8):

$$
m = \frac{8 - 10}{-3 - (-9)} = \frac{-2}{6} = -\frac{1}{3}
$$

Check (3, 6) and (9, 4):

$$
m = \frac{4 - 6}{9 - 3} = \frac{-2}{6} = -\frac{1}{3}
$$

✔ Consistent. So, $ m = -\frac{1}{3} $

---

⑥

| x | y |
|---|---|
| 3 | -1 |
| 6 | 1 |
| 9 | 3 |
| 12 | 5 |
| 15 | 7 |

Use (3, -1) and (6, 1):

$$
m = \frac{1 - (-1)}{6 - 3} = \frac{2}{3}
$$

Check (9, 3) and (12, 5):

$$
m = \frac{5 - 3}{12 - 9} = \frac{2}{3}
$$

✔ Consistent. So, $ m = \frac{2}{3} $

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✔ Final Answers:

1. $ m = -1 $
2. $ m = -2 $
3. $ m = 5 $
4. $ m = -\frac{1}{2} $
5. $ m = -\frac{1}{3} $
6. $ m = \frac{2}{3} $

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📝 Explanation:

The slope measures how much $ y $ changes for a unit change in $ x $. Since all tables show linear relationships, the slope is constant between any two points. We used the slope formula $ m = \frac{\Delta y}{\Delta x} $ and verified consistency across multiple pairs.

Let me know if you'd like this as a printable answer sheet!