Find the slope of the line satisfying the given conditions. through (5, 9) and (-2, 9)

Verified step by step guidance

1. Identify the coordinates of the two points given: \( (5, 9) \) and \( (-2, 9) \).
2. Recall the formula for the slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
3. Substitute the given points into the slope formula: \[ m = \frac{9 - 9}{-2 - 5} \]
4. Simplify the numerator and denominator separately: Numerator: \( 9 - 9 = 0 \) Denominator: \( -2 - 5 = -7 \)
5. Calculate the slope by dividing the simplified numerator by the denominator: \[ m = \frac{0}{-7} \] which simplifies to the slope value.

Key Concepts

Slope of a Line

The slope of a line measures its steepness and direction, calculated as the ratio of the change in y-values to the change in x-values between two points. It is often represented as 'm' and found using the formula m = (y2 - y1) / (x2 - x1).

Coordinate Points

Coordinate points are pairs of numbers (x, y) that represent locations on the Cartesian plane. Understanding how to use these points is essential for calculating the slope, as the difference between their x and y values determines the line's rise over run.

Horizontal Lines

A horizontal line has a constant y-value for all points, meaning its slope is zero. Recognizing when two points share the same y-coordinate helps quickly identify that the line is horizontal and the slope is zero without further calculation.