Ch. 2 - Graphs and Functions

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

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 68

Chapter 3, Problem 68

For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form. through (3, -5), parallel to y = 4

Verified step by step guidance

Identify the slope of the given line. The equation is $ y = 4 $, which is a horizontal line. This means the slope $ m = 0 $.

Since the new line is parallel to $ y = 4 $, it must also have the same slope $ m = 0 $.

Use the point-slope form of a line equation with the point $ (3, -5) $ and slope $ m = 0 $: $ y - y_1 = m(x - x_1) $. Substitute $ y_1 = -5 $, $ x_1 = 3 $, and $ m = 0 $ to get $ y - (-5) = 0(x - 3) $.

Simplify the equation to slope-intercept form $ y = mx + b $. Since $ m = 0 $, the equation becomes $ y = -5 $.

Convert the slope-intercept form $ y = -5 $ to standard form $ Ax + By = C $. Rearranging gives $ 0x + y = -5 $, or simply $ y = -5 $.

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-Intercept Form of a Line

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. It clearly shows the slope and where the line crosses the y-axis, making it easy to graph and understand the line's behavior.

Parallel Lines and Their Slopes

Parallel lines have identical slopes. If a line is parallel to y = 4, which is a horizontal line with slope 0, then the new line must also have slope 0, meaning it is horizontal.

Standard Form of a Line

The standard form of a line is Ax + By = C, where A, B, and C are integers, and A ≥ 0. It is useful for solving systems of equations and provides a different way to represent linear equations compared to slope-intercept form.

Recommended video:

Guided course

05:39

Standard Form of Line Equations

Related Practice

Textbook Question

For each function, find (a) ƒ(2) and (b) ƒ(-1).See Example 7. ƒ = {(2,5),(3,9),(-1,11),(5,3)}

views

Textbook Question

For each function, find (a) ƒ(2) and (b) ƒ(-1). ƒ = {(-1,3),(4,7),(0,6),(2,2)}

Textbook Question

Find and interpret the average rate of change illustrated in each graph.

Textbook Question

Graph each function.

$ƒ (x) = ∣ x ∣ - 3$

views

Textbook Question

Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. ƒ(x)=x²+2

Textbook Question

Solve each problem. A graph of y=ƒ(x) is shown in the standard viewing window. Which is the only value of x that could possibly be the solution of the equation ƒ(x) =0? A. -15 B. 0 C. 5 D. 15