Problem: Find the slope and distance between the points \( A(1, 2) \) and \( B(4, 6) \).

Solution: The slope \( m \) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 2}{4 - 1} = \frac{4}{3} \]

The distance \( d \) is calculated using the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

Problem: Find the slope and distance between the points \( C(3, -1) \) and \( D(7, 4) \).

Solution: The slope \( m \) is:

\[ m = \frac{4 - (-1)}{7 - 3} = \frac{5}{4} \]

The distance \( d \) is:

\[ d = \sqrt{(7 - 3)^2 + (4 - (-1))^2} = \sqrt{16 + 25} = \sqrt{41} \]

Problem: Find the slope and distance between the points \( P(0, 0) \) and \( Q(6, 8) \).

Solution: The slope \( m \) is:

\[ m = \frac{8 - 0}{6 - 0} = \frac{8}{6} = \frac{4}{3} \]

The distance \( d \) is:

\[ d = \sqrt{(6 - 0)^2 + (8 - 0)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \]

Problem: Find the slope and distance between the points \( A(-2, 3) \) and \( B(4, -1) \).

Solution: The slope \( m \) is:

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

The distance \( d \) is:

\[ d = \sqrt{(4 - (-2))^2 + (-1 - 3)^2} = \sqrt{36 + 16} = \sqrt{52} = 2\sqrt{13} \]

Problem: Find the slope and distance between the points \( E(1, -2) \) and \( F(5, 3) \).

Solution: The slope \( m \) is:

\[ m = \frac{3 - (-2)}{5 - 1} = \frac{5}{4} \]

The distance \( d \) is:

\[ d = \sqrt{(5 - 1)^2 + (3 - (-2))^2} = \sqrt{16 + 25} = \sqrt{41} \]

Problem: Find the slope and distance between the points \( G(3, 4) \) and \( H(6, 10) \).

Solution: The slope \( m \) is:

\[ m = \frac{10 - 4}{6 - 3} = \frac{6}{3} = 2 \]

The distance \( d \) is:

\[ d = \sqrt{(6 - 3)^2 + (10 - 4)^2} = \sqrt{9 + 36} = \sqrt{45} = 3\sqrt{5} \]

Problem: Find the slope and distance between the points \( I(-1, 4) \) and \( J(4, -2) \).

Solution: The slope \( m \) is:

\[ m = \frac{-2 - 4}{4 - (-1)} = \frac{-6}{5} \]

The distance \( d \) is:

\[ d = \sqrt{(4 - (-1))^2 + (-2 - 4)^2} = \sqrt{25 + 36} = \sqrt{61} \]