Question

(8, -1) and (6, -4)
(-11, -6) and (-8, -5)
(-5, 4) and (-5, 3)
(-2, -3) and (-5, 9)
(-3, 8) and (7, 8)
(-5, 3) and (7, -7)

Explanation:

To solve for the slope between each pair of points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

1. Points \((8, -1)\) and \((6, -4)\)

Step1: Identify coordinates

\(x_1 = 8, \, y_1 = -1\); \(x_2 = 6, \, y_2 = -4\)

Step2: Apply slope formula

\[
m = \frac{-4 - (-1)}{6 - 8} = \frac{-3}{-2} = \frac{3}{2}
\]

2. Points \((-11, -6)\) and \((-8, -5)\)

Step1: Identify coordinates

\(x_1 = -11, \, y_1 = -6\); \(x_2 = -8, \, y_2 = -5\)

Step2: Apply slope formula

\[
m = \frac{-5 - (-6)}{-8 - (-11)} = \frac{1}{3}
\]

3. Points \((-5, 4)\) and \((-5, 3)\)

Step1: Identify coordinates

\(x_1 = -5, \, y_1 = 4\); \(x_2 = -5, \, y_2 = 3\)

Step2: Apply slope formula

\[
m = \frac{3 - 4}{-5 - (-5)} = \frac{-1}{0} \, (\text{undefined, vertical line})
\]

4. Points \((-2, -3)\) and \((-5, 9)\)

Step1: Identify coordinates

\(x_1 = -2, \, y_1 = -3\); \(x_2 = -5, \, y_2 = 9\)

Step2: Apply slope formula

\[
m = \frac{9 - (-3)}{-5 - (-2)} = \frac{12}{-3} = -4
\]

5. Points \((-3, 8)\) and \((7, 8)\)

Step1: Identify coordinates

\(x_1 = -3, \, y_1 = 8\); \(x_2 = 7, \, y_2 = 8\)

Step2: Apply slope formula

\[
m = \frac{8 - 8}{7 - (-3)} = \frac{0}{10} = 0 \, (\text{horizontal line})
\]

6. Points \((-5, 3)\) and \((7, -7)\)

Step1: Identify coordinates

\(x_1 = -5, \, y_1 = 3\); \(x_2 = 7, \, y_2 = -7\)

Step2: Apply slope formula

\[
m = \frac{-7 - 3}{7 - (-5)} = \frac{-10}{12} = -\frac{5}{6}
\]

Final Slopes:

1. \(\boldsymbol{\frac{3}{2}}\)
2. \(\boldsymbol{\frac{1}{3}}\)
3. \(\boldsymbol{\text{undefined}}\)
4. \(\boldsymbol{-4}\)
5. \(\boldsymbol{0}\)
6. \(\boldsymbol{-\frac{5}{6}}\)

Answer:

To solve for the slope between each pair of points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

1. Points \((8, -1)\) and \((6, -4)\)

Step1: Identify coordinates

\(x_1 = 8, \, y_1 = -1\); \(x_2 = 6, \, y_2 = -4\)

Step2: Apply slope formula

\[
m = \frac{-4 - (-1)}{6 - 8} = \frac{-3}{-2} = \frac{3}{2}
\]

2. Points \((-11, -6)\) and \((-8, -5)\)

Step1: Identify coordinates

\(x_1 = -11, \, y_1 = -6\); \(x_2 = -8, \, y_2 = -5\)

Step2: Apply slope formula

\[
m = \frac{-5 - (-6)}{-8 - (-11)} = \frac{1}{3}
\]

3. Points \((-5, 4)\) and \((-5, 3)\)

Step1: Identify coordinates

\(x_1 = -5, \, y_1 = 4\); \(x_2 = -5, \, y_2 = 3\)

Step2: Apply slope formula

\[
m = \frac{3 - 4}{-5 - (-5)} = \frac{-1}{0} \, (\text{undefined, vertical line})
\]

4. Points \((-2, -3)\) and \((-5, 9)\)

Step1: Identify coordinates

\(x_1 = -2, \, y_1 = -3\); \(x_2 = -5, \, y_2 = 9\)

Step2: Apply slope formula

\[
m = \frac{9 - (-3)}{-5 - (-2)} = \frac{12}{-3} = -4
\]

5. Points \((-3, 8)\) and \((7, 8)\)

Step1: Identify coordinates

\(x_1 = -3, \, y_1 = 8\); \(x_2 = 7, \, y_2 = 8\)

Step2: Apply slope formula

\[
m = \frac{8 - 8}{7 - (-3)} = \frac{0}{10} = 0 \, (\text{horizontal line})
\]

6. Points \((-5, 3)\) and \((7, -7)\)

Step1: Identify coordinates

\(x_1 = -5, \, y_1 = 3\); \(x_2 = 7, \, y_2 = -7\)

Step2: Apply slope formula

\[
m = \frac{-7 - 3}{7 - (-5)} = \frac{-10}{12} = -\frac{5}{6}
\]

Final Slopes:

1. \(\boldsymbol{\frac{3}{2}}\)
2. \(\boldsymbol{\frac{1}{3}}\)
3. \(\boldsymbol{\text{undefined}}\)
4. \(\boldsymbol{-4}\)
5. \(\boldsymbol{0}\)
6. \(\boldsymbol{-\frac{5}{6}}\)