4.2 Graphing Linear Equations
A _ is an equation written in terms of x
and y, and can be written in the form: _.
A _ of an equation in two variables is an ordered
pair(x, y) that makes the equation true.
Example 1 Check solutions of Linear Equations
Deter
3.6 Solving Decimal Equations
Example 1 Round for the final answer.
Solve and round to the nearest hundredth.
-38x 39 = 118
Solve the equation. Round to the nearest hundredth.
1. 24x + 43 = 66
2. -42x + 28 = 87
3. 22x 39x
= 19
Example 2 Solving equations
4.1 The Coordinate Plane and Scatter Plots
A _ is formed by two real number
lines that intersect at a right angle at the _.
The horizontal axis is the _ and the vertical axis is
the _.
Each point in a coordinate plane corresponds to an
_ of real numbers.
4.4 Slope of a Line
Example 1 The Slope Ratio
Find the slope of a hill that has a vertical rise of 40 feet and a horizontal
run of 200 feet. Let m represent the slope.
The slope(m) of a line that passes through points () and (, ) is
m=
=
Example 2 Positiv
4.6 Graphing Lines Using Slope-Intercept Form
Slope Intercept Form:
y = mx + b
m = _, b = _
Example 1:
Find the slope and the y-intercept of 2x + y = -3.
*First, make sure the y is by itself
Find the slope and the y-intercept of each equation.
1) y x = 5
Chapter 5:
Writing Linear Equations
Mr. Baker
5.1 Writing Linear Equations in
Slope-Intercept Form
The slope-intercept form of an equation of a line with
slope _ and y-intercept _ is:
y = mx + b
Example 1
Write an equation for a line whose slope is 3 and
Chapter 6:
Solving and Graphing Linear
Inequalities
Mr. Baker
6.1: Solving One-Step Linear Inequalities
The graph of a linear inequality in one variable is the set of points on a number
line that represent all solutions of the inequality:
Verbal Phrase
In
4.5 Direct Variation
Model for Direct Variation: _ where k 0.
K is called the_.
Example 1 Write a Direct Variation Model.
The variables x and y vary directly. One pair of values is x = 5 and y =
20.
a. Write an equation that relates x and y.
b.
Find the v
Variables in Algebra(1.1)
Define:
variable value variable expression numerical expression evaluateVariable Expressions
8y, 8*y,(8)(y)
16 , 16 y,
y
Meaning
8 times y
16 divided by 8
Operation
Multiplication
Division
3+x
3 plus x
Addition
7t
7 minus t
Subt
1.3 Order of Operations
Definitions:
1) Order of Operations
2) Left to Right Rule -
Example 1: Evaluate without grouping symbols.
Evaluate the expression 3x2 + 1 when x = 4. Use the order of operations.
Example 2: Use the left to right rule.
Evaluate eac
1.4 Equations and Inequalities
Define:
Equation:
Inequality:
Solution:
Example 1:
Check to see if 2 and 3 are solutions of the equation 4x + 1 = 9.
Example 2: Solve equations with mental math
To solve equations with mental math, think of the equation as
1.5 Translating Words into Mathematical Symbols
Example 1 Translate Addition Phrases
Phrase
Translation
The sum of six and a number
_
8 more than a number
_
A number plus five
_
A number increased by seven
_
Example 2 Translate Subtraction Phrases
Phrase
1.6 A Problem Solving Plan Using Models
Example 1 Write an Algebraic Model
You and some friends are at a Chinese restaurant. You order several $2
plates of wontons, egg rolls, and dumplings. Your bill is $25.20, which
includes tax of $1.20. Use modeling t
1.8 An Introduction to Functions
A _ is a rule that establishes a relationship between
two quantities, called the _ and the _.
For each input value there is exactly one output value.
One way to describe a function is to make an_.
Example 1 - Make an input
2.1 The Real Number Line
Real numbers can be pictured as points on a line. Every real number is
either _, _, or _.
Real Number Line
The scale numbers on a real number line are equally spaced and
represent _. An integer is either positive, negative or
zero
4.3 Graphing Lines Using Intercepts
The _ is where the graph of a line crosses over the xaxis. The y-coordinate will be zero and the x-coordinate will be the
point where it crosses the x-axis.
The _ is where the graph of a line crosses over the yaxis. The
Variables in Algebra(1.1)
Define:
variable-
value-
variable expression-
numerical expression-
evaluate-
Variable Expressions
8y, 8*y,(8)(y)
16 , 16 y,
y
Meaning
8 times y
16 divided by 8
Operation
Multiplication
Division
3+x
3 plus x
Addition
7t
7 minus t
1.4 Equations and Inequalities
Define:
Equation:
Inequality:
Solution:
Example 1:
Check to see if 2 and 3 are solutions of the equation 4x + 1 = 9.
Example 2: Solve equations with mental math
To solve equations with mental math, think of the equation as
1.5 Translating Words into Mathematical Symbols
Example 1 Translate Addition Phrases
Phrase
Translation
The sum of six and a number
_
8 more than a number
_
A number plus five
_
A number increased by seven
_
Example 2 Translate Subtraction Phrases
Phrase
1.6 A Problem Solving Plan Using Models
Example 1 Write an Algebraic Model
You and some friends are at a Chinese restaurant. You order several $2
plates of wontons, egg rolls, and dumplings. Your bill is $25.20, which
includes tax of $1.20. Use modeling t
1.8 An Introduction to Functions
A _ is a rule that establishes a relationship between
two quantities, called the _ and the _.
For each input value there is exactly one output value.
One way to describe a function is to make an_.
Example 1 - Make an input
1.3 Order of Operations
Definitions:
1) Order of Operations
2) Left to Right Rule -
Example 1: Evaluate without grouping symbols.
Evaluate the expression 3x2 + 1 when x = 4. Use the order of operations.
Example 2: Use the left to right rule.
Evaluate eac
2.1 The Real Number Line
Real numbers can be pictured as points on a line. Every real number is
either _, _, or _.
Real Number Line
The scale numbers on a real number line are equally spaced and
represent _. An integer is either positive, negative or
zero
Addition Problem
5 + (-3)
-2 + (-6)
2.3 Subtracting Real Numbers
Equivalent Subtraction Problem
5-3
-2 6
Subtraction Rule
To subtract two real numbers, change the subtraction sign to a plus sign and change
the number behind the sign to its opposite.
Examp
2.2 Adding Real Numbers
You add a _ number by moving to the _ on
a number line.
You add a _ number by moving to the _ on
a number line.
Example 1 Add Using a Number Line
Use a number line to find the sum.
a. -2 + 5
b. 2 + (-6)
c. -3 + (-2)
_
Use the numbe
Section 2.4: Adding and Subtracting Matrices
A _ is a rectangular arrangement of numbers into horizontal rows
and vertical columns.
Each number in the matrix is called an _ or an _.
The size of a matrix is described as follows:
(the number of rows) X (the
2.6 The Distributive Property
The Distributive Property
The product of a and (b + c):
a(b + c) = ab + ac
Ex: 3(x + 7) = _
(b + c)a = ba + ca
Ex: (x + 5)6 = _
The product of a and (b c):
a(b c) = ab ac
Ex: 3(x 2) = _
(b c)a = ba bc
Ex: (x 4)8 = _
Example
3.1 Solving Equations Using Addition and Subtraction
Equivalent Equations
Original Equation
Equation
X3=5
_
X + 6 = 10
_
X=83
_
Action
Equivalent
_
_
_
Two operations that will undo each other, such as addition and
subtraction, are called _.
Example 1 Sol