Ch. 2 - Graphs and Functions

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

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 33

Chapter 3, Problem 33

Match each equation with the sketch that most closely resembles its graph. x = 5

Verified step by step guidance

Recognize that the equation \(x = 5\) represents a vertical line in the coordinate plane because it states that the x-coordinate is always 5 regardless of the y-coordinate.

Recall that vertical lines have the form \(x = a\), where \(a\) is a constant, and they run parallel to the y-axis.

Understand that the graph of \(x = 5\) will be a straight line crossing the x-axis at the point (5, 0).

Note that this line does not slope or curve; it extends infinitely up and down through all y-values while maintaining \(x = 5\).

When matching the equation to a sketch, look for the graph that shows a vertical line passing through \(x = 5\) on the x-axis.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Vertical Lines

A vertical line is a line where all points have the same x-coordinate. Its equation is of the form x = a constant, such as x = 5. This line runs parallel to the y-axis and does not depend on y-values.

Graphing Linear Equations

Graphing linear equations involves plotting all points (x, y) that satisfy the equation. For equations like x = 5, the graph is a straight line where x is fixed, illustrating the concept of lines with undefined slope.

Coordinate Plane and Axes

The coordinate plane consists of the x-axis (horizontal) and y-axis (vertical). Understanding the position of lines relative to these axes helps in matching equations to their graphs, such as recognizing that x = 5 is a vertical line crossing the x-axis at 5.

Recommended video:

Guided course

05:10

Graphs & the Rectangular Coordinate System

Related Practice

Textbook Question

Determine whether the three points are collinear. (0, 9),(-3, -7),(2, 19)

views

Textbook Question

Use the graph to evaluate each expression. See Example 3(a).

(ƒ+g)(2)

Textbook Question

Graph each function. See Examples 1 and 2. ƒ(x)=-√-x

Textbook Question

Determine whether each relation defines a function, and give the domain and range.

Textbook Question

Determine whether the three points are collinear. (-7,4),(6,-2),(-1,1)

Textbook Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. slope 0, y-intercept (0, 3/2)