Unit 5

Linear Functions

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Proportionality
Essential Question: What does the slope of a line indicate about a line?

Functions
Essential Question: What information does the equation of a line give you?

Modeling
Essential Question: How can you make predictions based on a scatter plot?

Ceteris Paribus
Essential Question: Loosely translated from Latin, ceteris paribus means "all other things held constant"  How can the analysis of functional relationships between two variables be useful when other variables impact the functional relationship, too?
 

FUNCTION
MACHINE

  DESMOS
Graphing Calculator

Lesson/Objective Supplemental Lessons On-line Practice Homework
5-1  Rate of Change and Slope

Objective:  To find rates of change from tables; To find slope

Essential Understandings: 
You can use ratios to show a relationship between changing quantities, such as vertical and horizontal change.

 

Video Tutors

finding the slope using rise over run

finding the rate of change using a table

finding the rate of change using a graph

finding slope using coordinates

finding the slope of horizontal or vertical lines
 


self-check quiz

Solve It!

Additional
PROBLEMS

Enrich!

hw#5-1: 
Due Monday, Jan 7
pg 297-299
 #1-10 All,
#11-21 Odd,
#23-25 All,
#27

SPECIAL LINKS from NY Regents Prep Website


SLOPE and RATE OF CHANGE

SKI BIRD helps you with SLOPE

5-2  Direct Variation

Postponed until later in the unit... Mr. C.

5-3  Slope-Intercept Form

Objective:  To write linear equations using slope-intercept form; To graph linear equations in slope-intercept form

Essential Understandings: 
You can use the slope and y-intercept of a line to write and graph an equation for the line.

 


Video Tutors

graphing a linear equation using slope-intercept form

writing an equation given the slope & y-intercept

writing an equation from a graph

small Purplemath hyperlink graphic

 


self-check quiz

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Additional
PROBLEMS

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hw#5-3: 
Due Wed Jan 9 

pg 312
#1-6 ALL
#7-27 ODD
5-4  Point-Slope Form

Objective: To write and graph linear equations using point-slope form

Essential Understandings: 
You can use the slope of a line and any point on the line to write and graph an equation of the line.  Any two equations for the same line are equivalent.

 


Video Tutors

analyzing linear graphs

graphing linear equations using point-slope form

writing an equation in point-slope form using a point and the slope

writing an equation in point-slope form from a graph

writing a linear equation using a table
 


self-check quiz

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Additional
PROBLEMS

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hw#5-4: 
Due Fri Jan 11
pg 318 
#1-7 ALL, 
#9-29 ODD
5-5  Standard Form

Objective: To graph linear equations using intercepts; To write linear equations in standard form

Essential Understandings: 
One form of a linear equation, called standard form, allows you to find intercepts quickly.  You can use the intercepts to draw the graph.
 

Video Tutors

Modeling real world situations using linear equations

Finding the x- and y-intercepts from an equation in standard form

Graphing linear equations using intercepts

small Purplemath hyperlink graphic

 


self-check quiz

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Additional
PROBLEMS

Enrich!

 

hw#5-5: 
Due Tues Jan 15

Complete Unit 5 Problem Set A

ANSWER KEY

AND (in your book)... 
pg 325-326
#1-7 ALL
#27-34 ALL


 

Mid-Chapter Practice and Review Use Slope-Intercept Form to Zap the Cockroaches!  

QUIZ on sections 5-1 thru 5-5 Thurs, Jan 17th

5-6  Parallel and Perpendicular Lines

Objective: To determine whether lines are parallel, perpendicular, or neither; To write equations of parallel lines and perpendicular lines

Essential Understandings: 
You can determine the relationship between two lines by comparing their slopes and y-intercepts. 

 

Video Tutors

Determining whether lines are parallel

Writing equations of parallel lines

Determining whether lines are perpendicular

Writing equations of perpendicular lines


self-check quiz

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Additional
PROBLEMS

Enrich!

 

hw#5-6: 
Due 
pg 330-32 #1-4 All
                 #7-35 Odd
 AND....
hw #5-2 
Due 

pg 302-03 # 1-5 All
                 #9-14 All
                 #30-34 All

 

 

5-2  Direct Variation

Objective:  To write and graph an equation of direct variation  

Essential Understandings: 
If the ration of two variables is constant, then the variables have a special relationship, known as a DIRECT VARIATION.

 


Video Tutors

using a direct variation to describe a situation

using a proportion as an equation of direct variation

using a proportion to solve a direct variation problem
 


self-check quiz

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Additional
PROBLEMS

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NOTE TO STUDENTS January, 2012
We will be SKIPPING SECTION 5-8 for now and re-visiting later in the year
I have left the section intact at the bottom of this page for my reference only

5-7  Scatter Plots and Trend Lines

Objective: To write an equation of a trend line and a line of best fit; To use a trend line and a line of best fit to make predictions

Essential Understandings: 
You can determine whether two sets of numerical data are related by graphing them as ordered pairs.  Most scatter plots are in the first quadrant of the coordinate plane because the data are usually positive numbers.

 

Video Tutors

Making a scatter plot

Using scatter plots and trend lines to make predictions

Writing an equation for a line of best fit


self-check quiz

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Additional
PROBLEMS

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hw#5-7: 
Due 

HOMEWORK
SMORGASBORD!!

Complete Unit 5 Problem Set B

pg 340-43 #9,10,18,19

For the UNIT TEST, you should IMMERSE yourself in pages 353-357. You don't have do to every problem, but YOU DO HAVE TO KNOW HOW TO DO EVERY PROBLEM!!

... AND, you should know where to ask questions if you need help.
 

UNIT TEST REVIEW UNIT 5 EXTRA PRACTICE

Answer Key

CUMULATIVE REVIEW 1-5  

UNIT 5 TEST (excluding section 5-8):  
TBA
N.B. LINE OF BEST FIT (using a graphing calculator) will NOT be on the test
TREND LINES will be on the test (you should know the difference!)

5-8  Graphing Absolute Value Functions

Objective: To graph an absolute value function; To translate the graph of an absolute value function

Essential Understandings: 
You can quickly graph absolute value equations by shifting the graph of y = |x|.

 

Video Tutors

Graphing a vertical translation of an absolute value equation

Writing an equation for the vertical translation of an absolute value equation

Graphing a horizontal translation of an absolute value equation

Writing an equation for the horizontal translation of absolute value equation
 


self-check quiz

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Additional
PROBLEMS

Enrich!

hw#5-8 Due 
pg 344-46
     #1-5 All
     #11- 41 Odd
     #50-53 All

Extra credit for the first few good explanations of #41 on the blog!