3-1 Graphing Linear Equations using a table...•3-1 Graphing Linear Equations using a table •3-2 Graphing Linear Equations using x and y intercepts •3-2b Graphing Linear Equations

• 3-1 Graphing Linear Equations using a table

• 3-2 Graphing Linear Equations using x and y intercepts

• 3-2b Graphing Linear Equations Using a TI-84 Calculator

• 3-3 Slope

• Mid-Chapter Review

• 3-4 Direct Variation

• 3-5 Arithmetic Sequences

• 3-6 Proportional and Non-proportional Relationships

• Chapter Review

Name:

Today we will:

∙ Identify linear equations, intercepts, and zeros. ∙ Graph Linear Functions.

Linea

r Eq

uatio

n

Stan

dard

Form

Define it

Cons

tant

Int

erce

pts

Let’s look at several examples of linear equations and some that are not linear.

Both variables must have the exponent of An equation cannot be linear if

Rem

em

ber

Linear Rules

Determine whether the following equations represents a linear function; if not, please explain why it is not linear.

You Try

A graph is a picture of the relationship between two variables, in our case, the variables x and y. The graph of a linear equation is a line. The line is made up of a series of points. You can use the equation to determine these points. Graph the following equations by using at least three points on the line.

Graphs of Equations

y= -2x+1 y = 3x-4

Practice

Wh

at’s

an

In

ter

cep

t?

DEFINE IT

Determine the x and y –intercept for the following linear functions: EX.1 𝟑𝒙 − 𝟒𝒚 = 𝟏𝟐 EX.2 𝟐𝒙 + 𝟑𝒚 = 𝟔

You Try

A graph is a picture of the relationship between two variables, in our case, the variables x and y. The graph of a linear equation is a line. The line is made up of a series of points. The x and y intercepts are two points on the line that can be used to graph it.

Graphs of Equations

7x-7y = 14 The x intercept is -2 and the y-intercept is 3.

Practice

Slope-Intercept

Graph the following functions, given their equations in y=mx+b form,

Graph Equations

y=-2x+4 y= 3x-1

Graph the following functions, given a point and its slope.

(-2 ,-3), m = 2/3 (1 , 2), m=-1

Direc

t V

ariatio

n How much money can Bianca earn in 5 hours of babysitting? How many hours of babysitting will it take for Bianca to earn $295? If Bianca cannot babysit that many hours what can she do to increase her income?

WH

Y?

See

top

of

pg. 1

80

Define it

In this lesson we will:

.Write and graph direct variation equations.

.Solve Problems involving direct variation.

y=kx, where k≠0 Name the constant of variation for each equation. Then find the slope of the line that passes through each pair of points.

Suppose x and y vary directly, and y=9, when x=-3. Write a direct variation equation that relates x and y.

y= kx Direct variation formula.

Replace y with _ and x with _.

Divide both sides by _.

Simplify.

Use the direct variation equation for find x when y = 15.

Direct variation formula.

Replace y with _ and x with _.

Divide both sides by _.

Simplify.

NAME:

Today we will: Recognize arithmetic sequences. Relate arithmetic sequences to linear functions.

3, 5, 7, 9, 11,...

A sequence is a set of numbers, called

terms, in a specific order. What is the pattern of this sequence?

Identify

-15,-13,-11,-9,... This is / is not an arithmetic sequence because the difference between the terms is _____.

7, 5, 1, -5, ... This is / is not an arithmetic sequence because the difference between the terms is _____.

The difference between the terms is call the

COMMON DIFFERENCE. It is expressed as “d.”

The arithmetic sequence 1, 10, 19, 28, … represents the total number of dollars Valentina has in her account after her weekly allowance is added.. a. Write an equations for the nth term of the sequence. In this sequence, the first term, a1, is 2. Find the common difference.

1 10 19 28 The common difference is . Use the formula for the nth term to write an equation. b. Find the 12th term in the sequence using the formula: an=9n-8, so a12= E

xp

licit

Fo

rm

ula

EX.1 15, 9, 3, -3, _ , _ , _ , _... EX.2 9.5, 11.0, 12.5, 14.0, _, _, _, _...

Try it

Write an explicit formula?

Write an explicit formula?

What’s the pattern?

Explicit Formula:

1. Let a1 be the first term of an arithmetic sequence with common difference, d.

2. Then the sequence is a1, a1 + d, a1+2d… a1 + (n-1) d

What’s the pattern?

Practice

Name: Today we will: Write an equation for proportional relationship. Write an equation for nonproportional relationship.

Define it

Proportional Relationships

Defin

itio

n

Ch

aracte

ris

tics

Exam

ple

s

Co

unte

r-E

xam

ple

Practice

Name: Today we will: Review the terms for Chapter 3

• Cut out the following foldables on the solid line and fold on the dotted lines.

• Under each Key term write/draw an example

X-I

nt

erce

pt

Y-I

nt

erce

pt

Zero/R

oot

Ra

te o

f

Cha

ng

e/S

lope

Name: Today we will: Review the terms for Chapter 3

• Cut out the following foldables on the solid line and fold on the dotted lines.

• Under each Key term write/draw an example

• In the middle describe how all these terms are related.

Y=kx K is the constant of

proportionality