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

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Recall that the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: \[m = \frac{y_2 - y_1}{x_2 - x_1}\]

Identify the coordinates of the two points given: $(x_1, y_1) = (5, 6)$ and $(x_2, y_2) = (5, -2)$.

Substitute the coordinates into the slope formula: \[m = \frac{-2 - 6}{5 - 5}\]

Simplify the numerator and denominator separately: Numerator: $-2 - 6 = -8$ Denominator: $5 - 5 = 0$

Interpret the result: since the denominator is zero, the slope is undefined, which means the line is vertical and does not have a defined slope.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Slope of a Line

The slope of a line measures its steepness and is calculated as the ratio of the change in y-values to the change in x-values between two points. It is given by the formula m = (y2 - y1) / (x2 - x1). A positive slope means the line rises, while a negative slope means it falls.

Vertical Lines and Undefined Slope

A vertical line has the same x-coordinate for all points, resulting in zero change in x. Since slope involves division by the change in x, this leads to division by zero, which is undefined. Therefore, vertical lines do not have a defined slope.

Coordinates of Points

Points on the coordinate plane are represented as (x, y). Understanding how to use these coordinates to find differences in x and y values is essential for calculating slope. In this problem, the points (5, 6) and (5, -2) share the same x-value, indicating a vertical line.

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