Worksheet for calculating slope from two points in algebra.

To find the slope of a line passing through two points, we use the slope formula:

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

Where:
- $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.
- $m$ is the slope.

Let’s solve each problem step by step.

---

1) (19, -16), (-7, -15)

$$
m = \frac{-15 - (-16)}{-7 - 19} = \frac{-15 + 16}{-26} = \frac{1}{-26} = -\frac{1}{26}
$$

✔ Slope: $-\frac{1}{26}$

---

2) (1, -19), (-2, -7)

$$
m = \frac{-7 - (-19)}{-2 - 1} = \frac{-7 + 19}{-3} = \frac{12}{-3} = -4
$$

✔ Slope: $-4$

---

3) (-4, 7), (-6, -4)

$$
m = \frac{-4 - 7}{-6 - (-4)} = \frac{-11}{-6 + 4} = \frac{-11}{-2} = \frac{11}{2}
$$

✔ Slope: $\frac{11}{2}$

---

4) (20, 8), (9, 16)

$$
m = \frac{16 - 8}{9 - 20} = \frac{8}{-11} = -\frac{8}{11}
$$

✔ Slope: $-\frac{8}{11}$

---

5) (17, -13), (17, 8)

$$
m = \frac{8 - (-13)}{17 - 17} = \frac{8 + 13}{0} = \frac{21}{0}
$$

⚠️ Division by zero → undefined slope

This means the line is vertical.

✔ Slope: undefined

---

6) (19, 3), (20, 3)

$$
m = \frac{3 - 3}{20 - 19} = \frac{0}{1} = 0
$$

✔ Slope: $0$ (horizontal line)

---

7) (3, 0), (-11, -15)

$$
m = \frac{-15 - 0}{-11 - 3} = \frac{-15}{-14} = \frac{15}{14}
$$

✔ Slope: $\frac{15}{14}$

---

8) (9, -2), (-11, 10)

$$
m = \frac{10 - (-2)}{-11 - 9} = \frac{10 + 2}{-20} = \frac{12}{-20} = -\frac{3}{5}
$$

✔ Slope: $-\frac{3}{5}$

---

✔ Final Answers:

| Problem | Slope |
|--------|-------|
| 1) | $-\frac{1}{26}$ |
| 2) | $-4$ |
| 3) | $\frac{11}{2}$ |
| 4) | $-\frac{8}{11}$ |
| 5) | undefined |
| 6) | $0$ |
| 7) | $\frac{15}{14}$ |
| 8) | $-\frac{3}{5}$ |

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