BIG IDEAS MATH Integrated Math 1: Student Edition 2016

16th Edition

ISBN: 9781680331127

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 5.6, Problem 44E

To determine

To graph: an inequality having some point on boundary line and some points are solutions of an inequality.

Expert Solution & Answer

Answer to Problem 44E

The shade the portion that does not contain the points (2,5),(−3,−5) .

Explanation of Solution

Given:

(2,5),(−3,−5) are on the boundary line.

(6,5),(−2,−3) are the solutions.

Concept used:

Graphing the inequalities, it will graph the ordinary linear functions just like it is done before. The difference is that a solution to the inequality is not the drawn line but coordinate plane that satisfy the inequality.

The boundary line is dashed for <or > and solid line for ≤or ≥ .

Calculation:

The objective is to find the linear inequation of two variables from the following properties.

(2,5),(−3,−5) are on the boundary line.

(6,5),(−2,−3) are the solutions.

following are the steps to write an inequality.

Step 1:

Write the slope from (6,5),(−2,−3) .

Slope:

(m)=change in ychange in x.m=−3−5−2−6=−8−8=1.

For y-intercept (b) :

Equation y=mx+b take a point which is solution (6,5) :

y=mx+b.5=1(6)+b.b=−1.

Linear equation is:

y=1(x)−1.y=x−1.

Step 2: As the value of y is always greater than or equal to x as clear from the equation.

Thus, the inequality is:

y>x−1.

Step 3 : check that the points (2,5)(−3,−5) satisfy the inequality.

y>x−1.5>2−1.y>x−1.−5>−3−1.

Line will be a dashed line as the symbol of strict inequality that is > .

Thus, the graph of the points satisfying the given conditions is given as:

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 5.6, Problem 44E

Hence, the shade the portion that does not contain the points (2,5),(−3,−5) .

Chapter 5.6, Problem 43E

Chapter 5.6, Problem 45E

Chapter 5 Solutions

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - Prob. 6E Ch. 5.2 - Prob. 7E Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - Prob. 10E Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Prob. 15E Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Prob. 18E Ch. 5.2 - Prob. 19E Ch. 5.2 - Prob. 20E Ch. 5.2 - Prob. 21E Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - Prob. 24E Ch. 5.2 - 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