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Let's solve each problem step by step.

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Problem 1:

We are given a table of points:

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

We need to find the slope of the line that passes through all these points.

#### Step 1: Recall the slope formula

The slope $ m $ between two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is:

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

We can pick any two points from the table. Let’s use the first two:

- Point A: $ (2, 2) $
- Point B: $ (3, 0) $

$$
m = \frac{0 - 2}{3 - 2} = \frac{-2}{1} = -2
$$

Now let’s check with another pair to make sure the slope is consistent.

Use $ (3, 0) $ and $ (4, -2) $:

$$
m = \frac{-2 - 0}{4 - 3} = \frac{-2}{1} = -2
$$

Another pair: $ (4, -2) $ and $ (5, -4) $:

$$
m = \frac{-4 - (-2)}{5 - 4} = \frac{-2}{1} = -2
$$

✔ All slopes are -2, so the slope is consistent.

#### ✔ Answer for Problem 1: $ \boxed{-2} $

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Problem 2:

Given table:

| x | y |
|---|---|
| 4 | 1 |
| 8 | 5 |
| 12 | 9 |
| 16 | 13 |
| 20 | 17 |
| 24 | 21 |

Again, we'll use the slope formula.

Pick the first two points:

- $ (4, 1) $ and $ (8, 5) $

$$
m = \frac{5 - 1}{8 - 4} = \frac{4}{4} = 1
$$

Check next pair: $ (8, 5) $ and $ (12, 9) $

$$
m = \frac{9 - 5}{12 - 8} = \frac{4}{4} = 1
$$

Next: $ (12, 9) $ and $ (16, 13) $

$$
m = \frac{13 - 9}{16 - 12} = \frac{4}{4} = 1
$$

Continue: $ (16, 13) $ and $ (20, 17) $

$$
m = \frac{17 - 13}{20 - 16} = \frac{4}{4} = 1
$$

Last: $ (20, 17) $ and $ (24, 21) $

$$
m = \frac{21 - 17}{24 - 20} = \frac{4}{4} = 1
$$

✔ Slope is consistently 1.

#### ✔ Answer for Problem 2: $ \boxed{1} $

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✔ Final Answers:

1. $ \boxed{-2} $
2. $ \boxed{1} $

These are both defined linear relationships with constant slopes.