Solution: Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):

\( m = \frac{8 - 4}{7 - 3} = \frac{4}{4} = 1 \)

The slope is \( m = 1 \).

Solution: Slope \( m = \tan(\theta) \):

\( m = \tan(30^\circ) \approx 0.577 \)

The slope is approximately \( m = 0.577 \).

Solution: First, calculate the slope of the original line:

\( m = \frac{15 - 5}{8 - 2} = \frac{10}{6} = \frac{5}{3} \)

The slope of any line parallel to this is also \( m = \frac{5}{3} \).

Solution: The slope of a perpendicular line is the negative reciprocal of the original slope:

\( m_{\text{perpendicular}} = -\frac{5}{4} \)

The perpendicular slope is \( m = -\frac{5}{4} \).

Solution: Rewrite in slope-intercept form \( y = mx + b \):

\( 3x - 4y = 12 \rightarrow y = \frac{3}{4}x - 3 \)

The slope is \( m = \frac{3}{4} \).

Solution: Slope \( m = \frac{\text{rise}}{\text{run}} \):

\( m = \frac{10}{3} \)

The slope is \( m = \frac{10}{3} \).

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

Since \( x_1 = x_2 \), the slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \) results in division by zero.

Solution: The angle \( \theta = \arctan(m) \):

\( \theta = \arctan(-1.5) \approx -56.31^\circ \)

Solution: The slope of the original line is \( m = -2 \).

The slope of a perpendicular line is \( m = \frac{1}{2} \).

Solution: Calculate the slope:

\( m = \frac{8 - 2}{4 - 1} = 2 \)

Since \( m > 0 \), the line is increasing.

Solution: Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):

\( m = \frac{5 - (-3)}{2 - (-4)} = \frac{8}{6} = \frac{4}{3} \)

The slope is \( m = \frac{4}{3} \).

Solution: The slope of the given line is \( m = 5 \). Any parallel line will have the same slope.

The slope of the parallel line is \( m = 5 \).

Solution: The slope of the given line is \( m = 3 \). The slope of a perpendicular line is the negative reciprocal:

\( m_{\text{perpendicular}} = -\frac{1}{3} \)

The perpendicular slope is \( m = -\frac{1}{3} \).

Solution: Rewrite the equation in slope-intercept form \( y = mx + b \):

\( 2x + 3y = 6 \rightarrow y = -\frac{2}{3}x + 2 \)

The slope is \( m = -\frac{2}{3} \).

Solution: Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1, y_1) = (0, 0) \):

\( m = \frac{8 - 0}{6 - 0} = \frac{8}{6} = \frac{4}{3} \)

The slope is \( m = \frac{4}{3} \).

Solution: The equation is already in slope-intercept form \( y = mx + b \), so the slope is \( m = -4 \).

The slope is \( m = -4 \).

Solution: Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):

\( m = \frac{6 - (-2)}{-3 - 5} = \frac{8}{-8} = -1 \)

The slope is \( m = -1 \).

Solution: Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):

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

The slope is \( m = -1 \).

Solution: Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):

\( m = \frac{10 - 0}{10 - 0} = \frac{10}{10} = 1 \)

The slope is \( m = 1 \).

Solution: Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):

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

The slope is \( m = -1 \).