Algebra 1 worksheet on finding the slope of lines from graphs and point pairs.

Let's solve each problem step by step.

---

Part 1: Find the slope of each line (from graphs)

We'll use the slope formula:

$$
\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
$$

We’ll pick two points on each line from the graph and compute the slope.

---

#### 1) First graph

Points on the line:
From the graph, we can see it passes through:
- $(-1, 3)$ and $(1, -1)$

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

✔ Answer: -2

---

#### 2) Second graph

Points:
It goes through:
- $(-2, -2)$ and $(2, 2)$

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

✔ Answer: 1

---

#### 3) Third graph

Vertical line passing through $x = -2$, from $y = -3$ to $y = 3$

This is a vertical line, so the slope is undefined.

> Because run = 0 → division by zero.

✔ Answer: undefined

---

#### 4) Fourth graph

Points:
It goes through:
- $(1, 3)$ and $(3, -1)$

$$
\text{slope} = \frac{-1 - 3}{3 - 1} = \frac{-4}{2} = -2
$$

✔ Answer: -2

---

#### 5) Fifth graph

Horizontal line at $y = -1$, from $x = -3$ to $x = 3$

This is a horizontal line, so slope is 0.

✔ Answer: 0

---

#### 6) Sixth graph

Points:
Passes through:
- $(-2, 3)$ and $(2, -1)$

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

✔ Answer: -1

---

Part 2: Find the slope through each pair of points

Use the same formula:

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

---

#### 7) $(-14, -20), (-5, 9)$

$$
m = \frac{9 - (-20)}{-5 - (-14)} = \frac{9 + 20}{-5 + 14} = \frac{29}{9}
$$

✔ Answer: $\frac{29}{9}$

---

#### 8) $(-1, 1), (5, -6)$

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

✔ Answer: $-\frac{7}{6}$

---

#### 9) $(15, 9), (-14, -9)$

$$
m = \frac{-9 - 9}{-14 - 15} = \frac{-18}{-29} = \frac{18}{29}
$$

✔ Answer: $\frac{18}{29}$

---

#### 10) $(2, -12), (18, 15)$

$$
m = \frac{15 - (-12)}{18 - 2} = \frac{15 + 12}{16} = \frac{27}{16}
$$

✔ Answer: $\frac{27}{16}$

---

✔ Final Answers:

| Problem | Answer |
|--------|---------------|
| 1 | -2 |
| 2 | 1 |
| 3 | undefined |
| 4 | -2 |
| 5 | 0 |
| 6 | -1 |
| 7 | $\frac{29}{9}$ |
| 8 | $-\frac{7}{6}$ |
| 9 | $\frac{18}{29}$ |
| 10 | $\frac{27}{16}$ |

Let me know if you'd like this formatted for printing or need explanations for any specific one!