Coordinate
Algebra
Unit 2: Reasoning
with Equations and
Inequalities
Excerpts from Georgia Department of
Education Webinar August 2, 2012
melissa.stewart@hallco.org
August 2012
Warm-Up
Two cyclists start at the same corner and
ride in opposite directions. One cyclist
rides twice as fast as the other. In 3
hours, they are 81 miles apart. Find the
rate of each cyclist.
Algebra practice can be found at
http://brightstorm.com/math/algebra/
melissa.stewart@hallco.org
August 2012
What’s the main idea of Unit 1?
• Developing a deeper understanding
and fluency in writing and solving
linear equations and inequalities.
• Developing a deeper understanding
in solving systems of equations and
interpreting their solutions.
melissa.stewart@hallco.org
August 2012
Concepts & Skills to Maintain from Previous Grades
(Same as Unit 1)
 Using the Pythagorean Theorem
 Understanding slope as a rate of change of one
quantity in relation to another quantity
 Interpreting a graph
 Creating a table of values
 Working with functions
 Writing a linear equation
 Using inverse operations to isolate variables and solve
equations
 Maintaining order of operations
 Understanding notation for inequalities
 Being able to read and write inequality symbols
 Graphing equations and inequalities on the coordinate
plane
 Understanding and using properties of exponents
 Graphing points
 Choosing appropriate scales and labeling a graph
Websites to help with the above:
http://www.crctlessons.com/
www.aplusmath.com
www.kidsnumbers.com
www.aaamath.com
melissa.stewart@hallco.org
August 2012
Enduring Understandings from this Unit
By the conclusion of this unit, students should be able to
 Solve linear equations and inequalities in one
variable
 Graph linear equations and inequalities in two
variables
 Solve systems of linear equations in two variables
exactly and approximately.
 Create linear equations and inequalities in one
variable and use them in a contextual situation to
solve problems
 Create equations in two or more variable to
represent relationships between quantities.

Graph equation in two variables on a coordinate
plane and label the axes and scales
melissa.stewart@hallco.org
August 2012
Examples & Explanations
1.
Jaden has a prepaid phone plan that
charges 15 cents for each text sent and 10
cents per minute for calls.
If Jaden wants to send 21 texts and only
has $6, how many minutes can he talk?
Will this use all of his money? If not, will
how much money will he have left? Justify
your answer.
.15t + .1c = Cost per month
.15(21) + .1c ≤ 6.00
3.15 + .1c ≤ 6.00
.1c ≤ 2.85
c ≤ 28.5
Jaden could talk for 28 minutes since most phone
companies charge for whole minutes and would
have 5 cents left.
melissa.stewart@hallco.org
August 2012
2.
Jose had 4 times as many trading cards as
Phillipe. After Jose gave away 50 cards to
his little brother and Phillipe gave 5 cards
to his friend for his birthday, they each had
an equal amount of cards. Write a system
to describe the situation.
SO,
J = 4P
P – 5 = J – 50
melissa.stewart@hallco.org
August 2012
3.
Fishing Adventures rents small fishing boats to tourists
for day long fishing trips. Each boat can hold at most
eight people. Additionally, each boat can only carry
1200 pounds of people and gear for safety reasons.
Assume on average an adult weighs 150 pounds and a
child weighs 75 pounds. Also assume each group will
require 200 pounds of gear plus 10 pounds of gear per
person. Can a group of 5 adults and 3 children safely
rent a boat?
The system would be:
a+c≤8
160a + 85c ≤ 1000
The sketch for the system is
Since the point (3,5) does NOT lie in the shaded
area, then, it is not safe.
melissa.stewart@hallco.org
August 2012
 The student edition for Unit 2 can be
found at
https://www.georgiastandards.org/C
ommon-Core/Pages/Math-9-12.aspx
On the left side, please look under
mathematics, Coordinate Algebra.
Then, the right side has a pull-down
menu to access the units.
 Additional parent guides will be
posted to the parent resource page on
http://www.hallco.org/boe/index.ph
p (right had menu) as they become
available.
melissa.stewart@hallco.org
August 2012