Find the slope of each line, provided that it has a slope. through (0, -7) and (3, -7)

Verified step by step guidance

1. Identify the formula for the slope of a line, which is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
2. Assign the coordinates of the points: \((x_1, y_1) = (0, -7)\) and \((x_2, y_2) = (3, -7)\).
3. Substitute the values into the slope formula: \( m = \frac{-7 - (-7)}{3 - 0} \).
4. Simplify the expression in the numerator: \(-7 - (-7) = 0\).
5. Calculate the slope: \( m = \frac{0}{3} \).

Key Concepts

Slope of a Line

The slope of a line measures its steepness and direction, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. It is often represented by the letter 'm' in the slope-intercept form of a linear equation, y = mx + b. A positive slope indicates the line rises from left to right, while a negative slope indicates it falls.

Coordinates of Points

Coordinates are pairs of numbers that define the position of points on a Cartesian plane. Each point is represented as (x, y), where 'x' is the horizontal position and 'y' is the vertical position. In the given question, the points (0, -7) and (3, -7) indicate that both points lie on the same horizontal line, which is crucial for determining the slope.

Horizontal Lines

A horizontal line is a straight line that runs left to right across the graph and has a constant y-value for all x-values. The slope of a horizontal line is always zero because there is no vertical change as you move along the line. In this case, since both points have the same y-coordinate (-7), the line connecting them is horizontal, resulting in a slope of 0.