Linear Equations worksheet with ten problems requiring students to find the slope and y-intercept from given points and write equations in slope-intercept form.

Of course! I'll solve each of the 10 problems step by step. For each, I’ll:

1. Calculate the slope $ m $ using the formula:
$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

2. Use one of the points and the slope to find the y-intercept $ b $ using:
$$
b = y - mx
$$

3. Write the final equation in slope-intercept form:
$$
y = mx + b
$$

---

Problem 1: Points (1, -7) and (-5, 0)

- Slope $ m = \frac{0 - (-7)}{-5 - 1} = \frac{7}{-6} = -\frac{7}{6} $
- Use point (1, -7):
$ b = -7 - (-\frac{7}{6})(1) = -7 + \frac{7}{6} = -\frac{42}{6} + \frac{7}{6} = -\frac{35}{6} $
- Equation:
$$
\boxed{y = -\frac{7}{6}x - \frac{35}{6}}
$$

---

Problem 2: Points (6, 9) and (-4, -2)

- Slope $ m = \frac{-2 - 9}{-4 - 6} = \frac{-11}{-10} = \frac{11}{10} $
- Use point (6, 9):
$ b = 9 - \frac{11}{10}(6) = 9 - \frac{66}{10} = \frac{90}{10} - \frac{66}{10} = \frac{24}{10} = \frac{12}{5} $
- Equation:
$$
\boxed{y = \frac{11}{10}x + \frac{12}{5}}
$$

---

Problem 3: Points (8, -6) and (6, 8)

- Slope $ m = \frac{8 - (-6)}{6 - 8} = \frac{14}{-2} = -7 $
- Use point (8, -6):
$ b = -6 - (-7)(8) = -6 + 56 = 50 $
- Equation:
$$
\boxed{y = -7x + 50}
$$

---

Problem 4: Points (4, 1) and (-6, 4)

- Slope $ m = \frac{4 - 1}{-6 - 4} = \frac{3}{-10} = -\frac{3}{10} $
- Use point (4, 1):
$ b = 1 - (-\frac{3}{10})(4) = 1 + \frac{12}{10} = 1 + \frac{6}{5} = \frac{11}{5} $
- Equation:
$$
\boxed{y = -\frac{3}{10}x + \frac{11}{5}}
$$

---

Problem 5: Points (6, -7) and (8, 5)

- Slope $ m = \frac{5 - (-7)}{8 - 6} = \frac{12}{2} = 6 $
- Use point (6, -7):
$ b = -7 - (6)(6) = -7 - 36 = -43 $
- Equation:
$$
\boxed{y = 6x - 43}
$$

---

Problem 6: Points (8, 7) and (-6, 4)

- Slope $ m = \frac{4 - 7}{-6 - 8} = \frac{-3}{-14} = \frac{3}{14} $
- Use point (8, 7):
$ b = 7 - \frac{3}{14}(8) = 7 - \frac{24}{14} = 7 - \frac{12}{7} = \frac{49}{7} - \frac{12}{7} = \frac{37}{7} $
- Equation:
$$
\boxed{y = \frac{3}{14}x + \frac{37}{7}}
$$

---

Problem 7: Points (5, -6) and (-4, 2)

- Slope $ m = \frac{2 - (-6)}{-4 - 5} = \frac{8}{-9} = -\frac{8}{9} $
- Use point (5, -6):
$ b = -6 - (-\frac{8}{9})(5) = -6 + \frac{40}{9} = -\frac{54}{9} + \frac{40}{9} = -\frac{14}{9} $
- Equation:
$$
\boxed{y = -\frac{8}{9}x - \frac{14}{9}}
$$

---

Problem 8: Points (-1, 6) and (8, 6)

- Slope $ m = \frac{6 - 6}{8 - (-1)} = \frac{0}{9} = 0 $ → horizontal line
- Since y is always 6, $ b = 6 $
- Equation:
$$
\boxed{y = 6}
$$

---

Problem 9: Points (2, 7) and (0, 7)

- Slope $ m = \frac{7 - 7}{0 - 2} = \frac{0}{-2} = 0 $ → horizontal line
- y is always 7, so $ b = 7 $
- Equation:
$$
\boxed{y = 7}
$$

---

Problem 10: Points (2, -7) and (-9, 9)

- Slope $ m = \frac{9 - (-7)}{-9 - 2} = \frac{16}{-11} = -\frac{16}{11} $
- Use point (2, -7):
$ b = -7 - (-\frac{16}{11})(2) = -7 + \frac{32}{11} = -\frac{77}{11} + \frac{32}{11} = -\frac{45}{11} $
- Equation:
$$
\boxed{y = -\frac{16}{11}x - \frac{45}{11}}
$$

---

✔ All 10 linear equations are now solved and written in $ y = mx + b $ form.

Let me know if you’d like to see graphs or verify any of these!