Find the slope of each line, provided that it has a slope. through (5, 6) and (5, -2)

Verified step by step guidance

1. The slope of a line is calculated using the formula: m = \frac{y_2 - y_1}{x_2 - x_1}.
2. Identify the coordinates of the two points: (x_1, y_1) = (5, 6) and (x_2, y_2) = (5, -2).
3. Substitute the coordinates into the slope formula: m = \frac{-2 - 6}{5 - 5}.
4. Simplify the expression in the numerator: -2 - 6 = -8.
5. Notice that the denominator is 0, which means the slope is undefined, indicating a vertical line.

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 in 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 (5, 6) and (5, -2) are used to determine the slope, highlighting the importance of understanding how to interpret these values.

Vertical Lines

A vertical line is defined by having the same x-coordinate for all points on the line, resulting in an undefined slope. In the context of the question, both points share the x-coordinate of 5, indicating that the line is vertical. This means that while we can identify the line's position, we cannot calculate a numerical slope, as it does not conform to the standard slope formula.