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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 31
Chapter 3, Problem 31

Match each equation with the sketch that most closely resembles its graph. y = 5
Four coordinate plane sketches labeled A to D, each showing a blue horizontal or vertical line on the x-y axes.

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1
Recognize that the equation \(y = 5\) represents a horizontal line because it is in the form \(y = c\), where \(c\) is a constant.
Understand that for every value of \(x\), the value of \(y\) remains constant at 5, so the graph is a straight line parallel to the x-axis.
Identify that the line will cross the y-axis at the point \((0, 5)\), which is the y-intercept.
Note that the slope of the line is 0, meaning there is no rise or fall as you move along the x-axis.
Match the equation \(y = 5\) with the sketch that shows a horizontal line passing through the y-coordinate 5.

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Key Concepts

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

Horizontal Lines

A horizontal line is a straight line where all points have the same y-coordinate. Its equation is of the form y = k, where k is a constant. For y = 5, the line passes through all points with y-coordinate 5, parallel to the x-axis.
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The Slope of a Line

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy the equation and connecting them. For equations like y = 5, the graph is a straight line. Understanding how to interpret and sketch these lines is essential for matching equations to their graphs.
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Categorizing Linear Equations

Coordinate Plane and Axes

The coordinate plane consists of the x-axis (horizontal) and y-axis (vertical). Knowing how to locate points and lines relative to these axes helps in visualizing graphs. For y = 5, the line is parallel to the x-axis and crosses the y-axis at 5.
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Graphs & the Rectangular Coordinate System
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