Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 47

Chapter 3, Problem 47

Find the slope of the line satisfying the given conditions. horizontal, through (5, 1)

Verified step by step guidance

Recall that a horizontal line has a slope of zero because it does not rise or fall as it moves from left to right.

Identify the given point through which the line passes, which is (5, 1).

Since the line is horizontal, its slope is the same everywhere along the line, regardless of the point.

Therefore, the slope of the line passing through (5, 1) and being horizontal is 0.

You can express the equation of this horizontal line as \(y = 1\), but the slope remains \(m = 0\).

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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 direction, calculated as the ratio of the change in y-values to the change in x-values between two points. It indicates how much y changes for a unit change in x.

Horizontal Lines

A horizontal line runs left to right and has no vertical change, meaning its slope is zero. All points on a horizontal line share the same y-coordinate, regardless of the x-coordinate.

Using a Point to Define a Line

A point on a line provides a specific location through which the line passes. When combined with the line's orientation (e.g., horizontal), it helps determine the equation or slope of the line.

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