Ch. 2 - Graphs and Functions

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

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 31

Chapter 3, Problem 31

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)

Verified step by step guidance

Identify the slope and y-intercept given in the problem. Here, the slope is 0, and the y-intercept is the point \( (0, \frac{3}{2}) \).

Recall that a slope of 0 means the line is horizontal. A horizontal line has the form \( y = b \), where \( b \) is the y-intercept.

Since the y-intercept is \( \frac{3}{2} \), the equation of the line in slope-intercept form is \( y = \frac{3}{2} \).

To write the equation in standard form, recall that standard form is \( Ax + By = C \), where \( A, B, \) and \( C \) are integers and \( A \geq 0 \).

Rewrite \( y = \frac{3}{2} \) as \( 0 \cdot x + y = \frac{3}{2} \), or simply \( y = \frac{3}{2} \), which is already in standard form with \( A=0, B=1, C=\frac{3}{2} \). If desired, multiply through by 2 to clear the fraction: \( 0 \cdot x + 2y = 3 \).

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.

Slope of a Line

The slope measures the steepness of a line and is defined as the ratio of the vertical change to the horizontal change between two points. A slope of 0 means the line is horizontal, indicating no vertical change as you move along the line.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, represented as (0, b). It indicates the value of y when x is zero and is essential for writing the equation of a line.

Forms of Linear Equations

Linear equations can be expressed in various forms, including standard form (Ax + By = C) and slope-intercept form (y = mx + b). The slope-intercept form explicitly shows the slope and y-intercept, while the standard form is a rearranged version often used for certain types of problems.

Recommended video:

06:00

Categorizing Linear Equations

Related Practice

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

Textbook Question

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

views

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.