Ch. 2 - Graphs and Functions

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

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 55

Chapter 3, Problem 55

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (4, 1), parallel to y=-5

Verified step by step guidance

Identify the given information: the line passes through the point (4, 1) and is parallel to the line given by the equation $y = -5$.

Recall that the equation $y = -5$ represents a horizontal line where the y-coordinate is always -5, so any line parallel to it is also horizontal and has the form $y = k$ for some constant $k$.

Since the new line passes through the point (4, 1), substitute the y-coordinate of this point into the general form of a horizontal line to find $k$. This gives $y = 1$.

Write the equation in standard form. For a horizontal line, the standard form is $y = 1$, which can also be written as $0x + y = 1$.

Write the equation in slope-intercept form, which is $y = mx + b$. Since the line is horizontal, the slope $m = 0$, so the equation is $y = 0x + 1$, simplifying to $y = 1$.

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.

Equation of a Horizontal Line

A horizontal line has a slope of zero and is represented by an equation of the form y = k, where k is the constant y-value for all points on the line. For example, y = -5 is a horizontal line passing through all points with y-coordinate -5.

Parallel Lines

Parallel lines have the same slope but different y-intercepts. Since the given line y = -5 is horizontal with slope 0, any line parallel to it must also have slope 0, meaning it is also horizontal.

Forms of Linear Equations

The standard form of a line is Ax + By = C, where A, B, and C are constants, and the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Converting between these forms helps express the line's equation clearly.

Recommended video:

06:00

Categorizing Linear Equations

Related Practice

Textbook Question

For each line, (a) find the slope and (b) sketch the graph. 5x - 2y = 10

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. ƒ(1/3)

views

Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=x²+3x+1

views

Textbook Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y=-|x+4|

views

Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

$ƒ (x) = x^{2} - 4 x + 2$

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. ƒ(-7/3)

views