High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
15th Edition
ISBN: 9780133281149
Author: Prentice Hall
Publisher: Prentice Hall
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Maximization
Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.
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Chapter 5.5, Problem 41PPE
To determine

To find: Graph of given equations and comparing them to express similarity among them.

Expert Solution & Answer
Check Mark

Answer to Problem 41PPE

Graph of all three given linear equations is shown below:

  High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9, Chapter 5.5, Problem 41PPE , additional homework tip 1

This graph depicts the similarity that two lines are parallel to each other or having the same slopes and another one is transversal to both.

Explanation of Solution

Given information: Three linear equations to graph each are 3x+y=6,  3x−y=6 and

  −3x+y=6 .

Concept/Formula used: A linear equation represents a line and a line is always drawn on joining any two points that are in ordered pair form (x,y) .

Calculation: Calculate any two points for each linear equation, as shown in below tables:

For equation 3x+y=6 ,

    x3x+y=6(x,y)
    03(0)+y=6y=6(0,6)
    23(2)+y=6y=6−6=0(2,0)

For equation, 3x−y=6

    x3x−y=6(x,y)
    03(0)−y=6y=−6(0,−6)
    23(2)−y=6y=6−6=0(2,0)

For equation, −3x+y=6

    x−3x+y=6(x,y)
    0−3(0)+y=6y=6(0,6)
    -2−3(−2)+y=6y=6−6=0(−2,0)

Plot these points in XY coordinate plane to get related graph as:

  High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9, Chapter 5.5, Problem 41PPE , additional homework tip 2

Conclusion: So, three lines are similar in the way that as lines −3x+y=6 and 3x−y=6 are shown parallel so their slopes are equal Also lines −3x+y=6 and 3x+y=6 as intersect each other at a single point, these two have a unique solution. Similarly lines 3x+y=6 and 3x−y=6 intersect each other at a single point on x axis, these two also have a unique solution

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Chapter 5 Solutions

High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9

Ch. 5.1 - Prob. 1PCh. 5.1 - Prob. 2PCh. 5.1 - Prob. 3PCh. 5.1 - Prob. 4PCh. 5.1 - Prob. 1LCCh. 5.1 - Prob. 2LCCh. 5.1 - Prob. 3LCCh. 5.1 - Prob. 4LCCh. 5.1 - Prob. 5LCCh. 5.1 - Prob. 6LC
Ch. 5.1 - Prob. 7LCCh. 5.1 - Prob. 8PPECh. 5.1 - Prob. 9PPECh. 5.1 - Prob. 10PPECh. 5.1 - Prob. 11PPECh. 5.1 - Prob. 12PPECh. 5.1 - Prob. 13PPECh. 5.1 - Prob. 14PPECh. 5.1 - Prob. 15PPECh. 5.1 - Prob. 16PPECh. 5.1 - Prob. 17PPECh. 5.1 - Prob. 18PPECh. 5.1 - Prob. 19PPECh. 5.1 - Prob. 20PPECh. 5.1 - Prob. 21PPECh. 5.1 - Prob. 22PPECh. 5.1 - Prob. 23PPECh. 5.1 - Prob. 24PPECh. 5.1 - Prob. 25PPECh. 5.1 - Prob. 26PPECh. 5.1 - Prob. 27PPECh. 5.1 - Prob. 28PPECh. 5.1 - Prob. 29PPECh. 5.1 - Prob. 30PPECh. 5.1 - Prob. 31PPECh. 5.1 - Prob. 32PPECh. 5.1 - Prob. 33PPECh. 5.1 - Prob. 34PPECh. 5.1 - Prob. 35PPECh. 5.1 - Prob. 36PPECh. 5.1 - Prob. 37PPECh. 5.1 - Prob. 38PPECh. 5.1 - Prob. 39PPECh. 5.1 - Prob. 40PPECh. 5.1 - Prob. 41PPECh. 5.1 - Prob. 42PPECh. 5.1 - Prob. 43PPECh. 5.1 - Prob. 44PPECh. 5.1 - Prob. 45PPECh. 5.1 - Prob. 46PPECh. 5.1 - Prob. 47PPECh. 5.1 - Prob. 48PPECh. 5.1 - Prob. 49PPECh. 5.1 - Prob. 50PPECh. 5.1 - Prob. 51PPECh. 5.1 - Prob. 52PPECh. 5.1 - Prob. 53PPECh. 5.1 - Prob. 54PPECh. 5.1 - Prob. 55PPECh. 5.1 - Prob. 56PPECh. 5.1 - Prob. 57PPECh. 5.1 - Prob. 58PPECh. 5.1 - Prob. 1MPCh. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 1LCCh. 5.2 - Prob. 2LCCh. 5.2 - Prob. 3LCCh. 5.2 - Prob. 4LCCh. 5.2 - Prob. 5LCCh. 5.2 - Prob. 6LCCh. 5.2 - Prob. 7LCCh. 5.2 - Prob. 8LCCh. 5.2 - Prob. 9PPECh. 5.2 - Prob. 10PPECh. 5.2 - Prob. 11PPECh. 5.2 - Prob. 12PPECh. 5.2 - Prob. 13PPECh. 5.2 - Prob. 14PPECh. 5.2 - Prob. 15PPECh. 5.2 - Prob. 16PPECh. 5.2 - Prob. 17PPECh. 5.2 - Prob. 18PPECh. 5.2 - Prob. 19PPECh. 5.2 - Prob. 20PPECh. 5.2 - Prob. 21PPECh. 5.2 - Prob. 22PPECh. 5.2 - Prob. 23PPECh. 5.2 - Prob. 24PPECh. 5.2 - Prob. 25PPECh. 5.2 - Prob. 26PPECh. 5.2 - Prob. 27PPECh. 5.2 - Prob. 28PPECh. 5.2 - Prob. 29PPECh. 5.2 - Prob. 30PPECh. 5.2 - Prob. 31PPECh. 5.2 - Prob. 32PPECh. 5.2 - Prob. 33PPECh. 5.2 - Prob. 34PPECh. 5.2 - Prob. 35PPECh. 5.2 - Prob. 36PPECh. 5.2 - Prob. 37PPECh. 5.2 - Prob. 38PPECh. 5.2 - Prob. 39PPECh. 5.2 - Prob. 40PPECh. 5.2 - Prob. 41PPECh. 5.2 - Prob. 42PPECh. 5.2 - Prob. 43PPECh. 5.2 - Prob. 44PPECh. 5.2 - Prob. 45PPECh. 5.2 - Prob. 46PPECh. 5.2 - Prob. 47PPECh. 5.2 - Prob. 48STPCh. 5.2 - Prob. 49STPCh. 5.2 - Prob. 50STPCh. 5.2 - Prob. 51STPCh. 5.2 - Prob. 52MRCh. 5.2 - Prob. 53MRCh. 5.2 - Prob. 54MRCh. 5.2 - Prob. 55MRCh. 5.2 - Prob. 56MRCh. 5.2 - Prob. 57MRCh. 5.2 - Prob. 58MRCh. 5.2 - Prob. 59MRCh. 5.3 - Prob. 1CBCh. 5.3 - Prob. 2CBCh. 5.3 - Prob. 3CBCh. 5.3 - Prob. 4CBCh. 5.3 - Prob. 5CBCh. 5.3 - Prob. 6CBCh. 5.3 - Prob. 7CBCh. 5.3 - Prob. 1PCh. 5.3 - Prob. 2PCh. 5.3 - Prob. 3PCh. 5.3 - Prob. 4PCh. 5.3 - Prob. 5PCh. 5.3 - Prob. 6PCh. 5.3 - Prob. 1LCCh. 5.3 - Prob. 2LCCh. 5.3 - Prob. 3LCCh. 5.3 - Prob. 4LCCh. 5.3 - Prob. 5LCCh. 5.3 - Prob. 6LCCh. 5.3 - Prob. 7PPECh. 5.3 - Prob. 8PPECh. 5.3 - Prob. 9PPECh. 5.3 - Prob. 10PPECh. 5.3 - Prob. 11PPECh. 5.3 - Prob. 12PPECh. 5.3 - Prob. 13PPECh. 5.3 - Prob. 14PPECh. 5.3 - Prob. 15PPECh. 5.3 - Prob. 16PPECh. 5.3 - Prob. 17PPECh. 5.3 - Prob. 18PPECh. 5.3 - Prob. 19PPECh. 5.3 - Prob. 20PPECh. 5.3 - 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Prob. 5MCQCh. 5.4 - Prob. 6MCQCh. 5.4 - Prob. 7MCQCh. 5.4 - Prob. 8MCQCh. 5.4 - Prob. 9MCQCh. 5.4 - Prob. 10MCQCh. 5.4 - Prob. 11MCQCh. 5.4 - Prob. 12MCQCh. 5.4 - Prob. 13MCQCh. 5.4 - Prob. 14MCQCh. 5.4 - Prob. 15MCQCh. 5.4 - Prob. 16MCQCh. 5.4 - Prob. 17MCQCh. 5.4 - Prob. 18MCQCh. 5.4 - Prob. 19MCQCh. 5.4 - Prob. 20MCQCh. 5.4 - Prob. 21MCQCh. 5.4 - Prob. 22MCQCh. 5.4 - Prob. 23MCQCh. 5.4 - Prob. 24MCQCh. 5.4 - Prob. 25MCQCh. 5.4 - Prob. 26MCQCh. 5.5 - Prob. 1PCh. 5.5 - Prob. 2PCh. 5.5 - Prob. 3PCh. 5.5 - Prob. 4PCh. 5.5 - Prob. 5PCh. 5.5 - Prob. 1LCCh. 5.5 - Prob. 2LCCh. 5.5 - Prob. 3LCCh. 5.5 - Prob. 4LCCh. 5.5 - Prob. 5LCCh. 5.5 - Prob. 6LCCh. 5.5 - Prob. 7LCCh. 5.5 - Prob. 8PPECh. 5.5 - Prob. 9PPECh. 5.5 - Prob. 10PPECh. 5.5 - Prob. 11PPECh. 5.5 - Prob. 12PPECh. 5.5 - Prob. 13PPECh. 5.5 - Prob. 14PPECh. 5.5 - Prob. 15PPECh. 5.5 - Prob. 16PPECh. 5.5 - Prob. 17PPECh. 5.5 - Prob. 18PPECh. 5.5 - Prob. 19PPECh. 5.5 - Prob. 20PPECh. 5.5 - Prob. 21PPECh. 5.5 - Prob. 22PPECh. 5.5 - Prob. 23PPECh. 5.5 - Prob. 24PPECh. 5.5 - Prob. 25PPECh. 5.5 - Prob. 26PPECh. 5.5 - Prob. 27PPECh. 5.5 - Prob. 28PPECh. 5.5 - Prob. 29PPECh. 5.5 - Prob. 30PPECh. 5.5 - Prob. 31PPECh. 5.5 - Prob. 32PPECh. 5.5 - Prob. 33PPECh. 5.5 - Prob. 34PPECh. 5.5 - Prob. 35PPECh. 5.5 - Prob. 36PPECh. 5.5 - Prob. 37PPECh. 5.5 - Prob. 38PPECh. 5.5 - Prob. 39PPECh. 5.5 - Prob. 40PPECh. 5.5 - Prob. 41PPECh. 5.5 - Prob. 42PPECh. 5.5 - Prob. 43PPECh. 5.5 - Prob. 44PPECh. 5.5 - Prob. 45PPECh. 5.5 - Prob. 46PPECh. 5.5 - Prob. 47PPECh. 5.5 - Prob. 48PPECh. 5.5 - Prob. 49PPECh. 5.5 - Prob. 50PPECh. 5.5 - Prob. 51PPECh. 5.5 - Prob. 52PPECh. 5.5 - Prob. 53PPECh. 5.5 - Prob. 54PPECh. 5.5 - Prob. 55PPECh. 5.5 - Prob. 56PPECh. 5.5 - Prob. 57PPECh. 5.5 - Prob. 58PPECh. 5.5 - Prob. 59PPECh. 5.5 - Prob. 60PPECh. 5.5 - Prob. 61PPECh. 5.5 - Prob. 62PPECh. 5.5 - Prob. 63PPECh. 5.5 - Prob. 64STPCh. 5.5 - Prob. 65STPCh. 5.5 - Prob. 66STPCh. 5.5 - Prob. 67STPCh. 5.5 - Prob. 68STPCh. 5.5 - Prob. 69MRCh. 5.5 - Prob. 70MRCh. 5.5 - Prob. 71MRCh. 5.5 - Prob. 72MRCh. 5.5 - Prob. 73MRCh. 5.5 - Prob. 74MRCh. 5.5 - Prob. 75MRCh. 5.5 - Prob. 76MRCh. 5.5 - Prob. 77MRCh. 5.5 - Prob. 1CBCh. 5.5 - Prob. 2CBCh. 5.5 - Prob. 3CBCh. 5.5 - Prob. 4CBCh. 5.5 - Prob. 5CBCh. 5.5 - Prob. 6CBCh. 5.5 - Prob. 7CBCh. 5.5 - Prob. 8CBCh. 5.5 - Prob. 9CBCh. 5.5 - Prob. 10CBCh. 5.5 - Prob. 11CBCh. 5.5 - Prob. 12CBCh. 5.5 - Prob. 13CBCh. 5.5 - Prob. 14CBCh. 5.5 - Prob. 15CBCh. 5.5 - Prob. 16CBCh. 5.5 - Prob. 17CBCh. 5.5 - Prob. 18CBCh. 5.5 - Prob. 19CBCh. 5.6 - Prob. 1PCh. 5.6 - Prob. 2PCh. 5.6 - Prob. 3PCh. 5.6 - Prob. 4PCh. 5.6 - Prob. 1LCCh. 5.6 - Prob. 2LCCh. 5.6 - Prob. 3LCCh. 5.6 - Prob. 4LCCh. 5.6 - Prob. 5LCCh. 5.6 - Prob. 6LCCh. 5.6 - Prob. 7PPECh. 5.6 - Prob. 8PPECh. 5.6 - Prob. 9PPECh. 5.6 - Prob. 10PPECh. 5.6 - Prob. 11PPECh. 5.6 - Prob. 12PPECh. 5.6 - Prob. 13PPECh. 5.6 - Prob. 14PPECh. 5.6 - Prob. 15PPECh. 5.6 - Prob. 16PPECh. 5.6 - Prob. 17PPECh. 5.6 - Prob. 18PPECh. 5.6 - Prob. 19PPECh. 5.6 - Prob. 20PPECh. 5.6 - Prob. 21PPECh. 5.6 - Prob. 22PPECh. 5.6 - Prob. 23PPECh. 5.6 - Prob. 24PPECh. 5.6 - Prob. 25PPECh. 5.6 - Prob. 26PPECh. 5.6 - Prob. 27PPECh. 5.6 - Prob. 28PPECh. 5.6 - Prob. 29PPECh. 5.6 - Prob. 30PPECh. 5.6 - Prob. 31PPECh. 5.6 - Prob. 32PPECh. 5.6 - Prob. 33PPECh. 5.6 - Prob. 34PPECh. 5.6 - Prob. 35PPECh. 5.6 - Prob. 36PPECh. 5.6 - Prob. 37PPECh. 5.6 - Prob. 38STPCh. 5.6 - Prob. 39STPCh. 5.6 - Prob. 40STPCh. 5.6 - Prob. 41MRCh. 5.6 - Prob. 42MRCh. 5.6 - Prob. 43MRCh. 5.6 - Prob. 44MRCh. 5.6 - Prob. 45MRCh. 5.6 - Prob. 46MRCh. 5.6 - Prob. 47MRCh. 5.7 - Prob. 1PCh. 5.7 - Prob. 2PCh. 5.7 - Prob. 3PCh. 5.7 - Prob. 4PCh. 5.7 - Prob. 1LCCh. 5.7 - Prob. 2LCCh. 5.7 - Prob. 3LCCh. 5.7 - Prob. 4LCCh. 5.7 - Prob. 5LCCh. 5.7 - Prob. 6LCCh. 5.7 - Prob. 7PPECh. 5.7 - Prob. 8PPECh. 5.7 - Prob. 9PPECh. 5.7 - Prob. 10PPECh. 5.7 - Prob. 11PPECh. 5.7 - Prob. 12PPECh. 5.7 - Prob. 13PPECh. 5.7 - Prob. 14PPECh. 5.7 - Prob. 15PPECh. 5.7 - Prob. 16PPECh. 5.7 - Prob. 17PPECh. 5.7 - Prob. 18PPECh. 5.7 - Prob. 19PPECh. 5.7 - Prob. 20PPECh. 5.7 - Prob. 21PPECh. 5.7 - Prob. 22PPECh. 5.7 - Prob. 23STPCh. 5.7 - Prob. 24STPCh. 5.7 - Prob. 25STPCh. 5.7 - Prob. 26STPCh. 5.7 - Prob. 27MRCh. 5.7 - Prob. 28MRCh. 5.7 - Prob. 29MRCh. 5.7 - Prob. 30MRCh. 5.7 - Prob. 31MRCh. 5.7 - Prob. 32MRCh. 5.7 - Prob. 33MRCh. 5.7 - Prob. 5CBCh. 5.7 - Prob. 6CBCh. 5.8 - Prob. 1PCh. 5.8 - Prob. 2PCh. 5.8 - Prob. 3PCh. 5.8 - Prob. 4PCh. 5.8 - Prob. 1LCCh. 5.8 - Prob. 2LCCh. 5.8 - Prob. 3LCCh. 5.8 - Prob. 4LCCh. 5.8 - Prob. 5LCCh. 5.8 - Prob. 6PPECh. 5.8 - Prob. 7PPECh. 5.8 - Prob. 8PPECh. 5.8 - Prob. 9PPECh. 5.8 - Prob. 10PPECh. 5.8 - Prob. 11PPECh. 5.8 - Prob. 12PPECh. 5.8 - Prob. 13PPECh. 5.8 - Prob. 14PPECh. 5.8 - Prob. 15PPECh. 5.8 - Prob. 16PPECh. 5.8 - Prob. 17PPECh. 5.8 - Prob. 18PPECh. 5.8 - Prob. 19PPECh. 5.8 - Prob. 20PPECh. 5.8 - Prob. 21PPECh. 5.8 - Prob. 22PPECh. 5.8 - Prob. 23PPECh. 5.8 - Prob. 24PPECh. 5.8 - Prob. 25PPECh. 5.8 - Prob. 26PPECh. 5.8 - Prob. 27PPECh. 5.8 - Prob. 28PPECh. 5.8 - Prob. 29PPECh. 5.8 - Prob. 30PPECh. 5.8 - Prob. 31PPECh. 5.8 - Prob. 32PPECh. 5.8 - Prob. 33PPECh. 5.8 - Prob. 34PPECh. 5.8 - Prob. 35PPECh. 5.8 - Prob. 36PPECh. 5.8 - Prob. 37PPECh. 5.8 - Prob. 38STPCh. 5.8 - Prob. 39STPCh. 5.8 - Prob. 40STPCh. 5.8 - Prob. 41STPCh. 5.8 - Prob. 42MRCh. 5.8 - Prob. 43MRCh. 5.8 - Prob. 44MRCh. 5.8 - Prob. 45MRCh. 5.8 - Prob. 46MRCh. 5.8 - Prob. 47MRCh. 5.8 - Prob. 1CBCh. 5.8 - Prob. 2CBCh. 5 - Prob. 1GRCh. 5 - Prob. 2GRCh. 5 - Prob. 3GRCh. 5 - Prob. 4GRCh. 5 - Prob. 5GRCh. 5 - Prob. 6GRCh. 5 - Prob. 7GRCh. 5 - Prob. 8GRCh. 5 - Prob. 9GRCh. 5 - Prob. 10GRCh. 5 - Prob. 11GRCh. 5 - Prob. 12GRCh. 5 - Prob. 13GRCh. 5 - Prob. 14GRCh. 5 - Prob. 15GRCh. 5 - Prob. 16GRCh. 5 - Prob. 17GRCh. 5 - Prob. 1CRCh. 5 - Prob. 2CRCh. 5 - Prob. 3CRCh. 5 - Prob. 4CRCh. 5 - Prob. 5CRCh. 5 - Prob. 6CRCh. 5 - Prob. 7CRCh. 5 - Prob. 8CRCh. 5 - Prob. 9CRCh. 5 - Prob. 10CRCh. 5 - Prob. 11CRCh. 5 - Prob. 12CRCh. 5 - Prob. 13CRCh. 5 - Prob. 14CRCh. 5 - Prob. 15CRCh. 5 - Prob. 16CRCh. 5 - Prob. 17CRCh. 5 - Prob. 18CRCh. 5 - Prob. 19CRCh. 5 - Prob. 20CRCh. 5 - Prob. 21CRCh. 5 - Prob. 22CRCh. 5 - Prob. 23CRCh. 5 - Prob. 24CRCh. 5 - Prob. 25CRCh. 5 - Prob. 26CRCh. 5 - Prob. 27CRCh. 5 - Prob. 28CRCh. 5 - Prob. 29CRCh. 5 - Prob. 30CRCh. 5 - Prob. 31CRCh. 5 - Prob. 32CRCh. 5 - Prob. 33CRCh. 5 - Prob. 34CRCh. 5 - Prob. 35CRCh. 5 - Prob. 36CRCh. 5 - Prob. 37CRCh. 5 - Prob. 38CRCh. 5 - Prob. 39CRCh. 5 - Prob. 40CRCh. 5 - Prob. 1CTCh. 5 - Prob. 2CTCh. 5 - Prob. 3CTCh. 5 - Prob. 4CTCh. 5 - Prob. 5CTCh. 5 - Prob. 6CTCh. 5 - Prob. 7CTCh. 5 - Prob. 8CTCh. 5 - Prob. 9CTCh. 5 - Prob. 10CTCh. 5 - Prob. 11CTCh. 5 - Prob. 12CTCh. 5 - Prob. 13CTCh. 5 - Prob. 14CTCh. 5 - Prob. 15CTCh. 5 - Prob. 16CTCh. 5 - Prob. 17CTCh. 5 - Prob. 18CTCh. 5 - Prob. 19CTCh. 5 - Prob. 20CTCh. 5 - Prob. 21CTCh. 5 - Prob. 22CTCh. 5 - Prob. 23CTCh. 5 - Prob. 1CCSRCh. 5 - Prob. 2CCSRCh. 5 - Prob. 3CCSRCh. 5 - Prob. 4CCSRCh. 5 - Prob. 5CCSRCh. 5 - Prob. 6CCSRCh. 5 - Prob. 7CCSRCh. 5 - Prob. 8CCSRCh. 5 - Prob. 9CCSRCh. 5 - Prob. 10CCSRCh. 5 - Prob. 11CCSRCh. 5 - Prob. 12CCSRCh. 5 - Prob. 13CCSRCh. 5 - Prob. 14CCSRCh. 5 - 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