Entire unit, or else Homework Club will be assigned. ➢ If you cannot ... 10/25/12 (
A) ... Objective #1: Can you write the equation of a line in slope-intercept form?
Name:________________________________
Assignments for Algebra 1 Unit 4: Linear Functions and Correlation Day
Date
Thursday Monday Tuesday Wednesday Thursday Friday Monday Wednesday Thursday Friday Tuesday Wednesday
10/25/12 (A) 10/29/12 (B) 10/30/12 (A) 10/31/12 (B) 11/01/12 (A) 11/02/12 (B) 11/05/12 (A) 11/07/12 (B) 11/08/12 (A) 11/09/12 (B) 11/13/12 (A) 11/14/12 (B)
Assignment (Due the next class meeting) 4.1 Worksheet 4.2 Worksheet 4.3 Worksheet 4.4 Worksheet Unit 4 Practice Test Unit 4 Exam/Begin Unit 5
Be prepared for daily quizzes! Every student is expected to do every assignment for the Entire unit, or else Homework Club will be assigned. If you cannot solve a problem, get help before the assignment is due. See your math teacher for assistance. Khanacademy.com can be helpful if you need assistance outside of school hours.
.
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4.1: Writing Linear Functions How can you represent a function or equation in slope intercept form? Warm-Up: 1) Find the slope through The given points (-2,4) and (6,-2)
2) Solve:
3) Graph the line:
4.1 Writing Linear Equations in Slope-Intercept Form Slope-Intercept Form:
(y = ____x + _____)
can be used to write an equation of a line
if the slope and y-intercept are given or can be found. As a function the equation looks almost the same. f(x)
= _____x + ______
Remember: m represents the ________ and b represents the ____-__________________
Example: Use slope and y-intercept to write an equation or function. Write an equation of the line with a slope of -4 and a y-intercept of 6. Solution: Write slope-intercept form
Substitute ______ for m and ______ for b.
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y = mx + b
y = ___x + ___
Examples: Writing equations of a line given slope and y-intercept.
Writing linear functions when given a
1. Slope is 8; y-intercept is -5
Write the linear function f using the given
slope and intercept
information. 1) The graph of a function has a slope of 3 and a y-intercept of -1.
2. Slope is ; y-intercept is -2 2) The graph of a function has a slope of and a y-intercept of -3.
Objective #1: Can you write the equation of a line in slope-intercept form? (for c and d use function notation f(x) = mx + b. a) slope = 6, y-intercept = -8
c) slope = 1, y-intercept = 3
b) slope = ½, y-intercept = 0
c) slope = - , y-intercept = -2
Reflection 1 What two things do you need to know to write an equation of a line?
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Example: Writing equations of a line from a graph. Solution: Step 1: Calculate the slope using
.
Step 2: Find the y-intercept. The line crosses the y-axis at _________. So the y-intercept is ______. (Write in slope intercept form) (Substitute ____for m and ____ for b)
y = mx + b
y = ___x + ___
Examples: Write an equation of the line shown below. For #2 use function notation, f(x) = mx + b. 1)
2)
Objective #2: Can you write the equation of a line in slope-intercept form from a graph. a.) Write an equation of the line shown.
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b.) Write a linear function for the line shown.
Example: Writing equations of horizontal and vertical lines. 1) Write an equation for each line from the graph.
2) Write an equation for each line in the graph below.
Line A:
Line A:
Line B: Line B:
3) Write the equation of both the vertical and horizontal line through the point (-4, 8)
Objective #3: Can you write the equation of a vertical and horizontal line.
Write an equation for the vertical and horizontal line through the given point. a.) (3, -7)
b.) (-5, 8)
Horizontal:
Horizontal:
Vertical:
Vertical:
Reflection #2 How do equations of horizontal and vertical lines look different than the equation of a line in slope-intercept form?
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Word Problems: Write an equation to model the situation. 1.) Jack and Jill decided to go bowling on a Sunday afternoon, if it cost $2.50 per game and $5.50 for their shoe rentals, write an equation that represents their total cost, y, if they bowl x number of games.
2.) Freddy and Alex decided to go to the state fair and go on the rides, if they spent $6.00 to park and $2.00 per ride, write an equation that shows the total amount spent at the fair. Writing linear functions when given a verbal description 1) Three pounds of squid can be purchased at the market for $18 and the fish market charges a flat fee of $5 for packaging. Determine the equation and represent the function for total cost C according to the price of squid as a function weight. How much does the squid cost per pound? What is the fixed cost? Write the function.
2) It has been observed that a particular plant's growth is directly proportional to time. It measured 2 cm when it arrived at the nursery and 3.5 cm exactly one week later. If the plant continues to grow at this rate, write a linear function for the total height of the plant, h, that represents the plant's height as a function of time. (Use the height when it arrived as the starting value)
Objective 4: Can you write a linear function in the form f(x) = mx + b when given a verbal description?
A salesperson earns a base salary of $35,000 per year and receives a commission of 10% of their sales for the year. Write a linear function for total money earned for the year, t, as a function of their sales for the year.
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4.2 Writing Linear Equations
How can you write linear equations or functions when given a two points on the line?
1. Find the slope between each pair of points: a.) (7, 9) and (5, 12) b.) (-2, 8) and (6, -4)
2. Solve for y in the given equation: a.) 𝟑𝒙 𝟐𝒚 𝟔
𝟐𝒙
b.)
𝟑𝒚
𝟐𝒙
𝟗
Point-Slope Form:
(
), where
is the slope and (
) is any point on the line.
Writing an equation of a line in point-slope form: Step 1: Identify the slope______. You can use the ___________ _____________ to calculate the slope if you know two points on the line.
Step 2: Use one of the points (
) and the slope to substitute into the point-slope
formula. (
)
Example: Write the equation of a line given slope and a point. Write an equation of a line that passes through the point (1, 2) and has a slope of 3.
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*Examples: Write an equation for each line below in Point-Slope form. 1.) passes through (-2, 5) with a slope of .
2.) passes through (2, -3) and (-2, 1).
3.) passes through (-3,-3) and (6,0).
4.) passes through (-3, 5) and (2, -10)
Sometimes the ordered pairs are given in function notation. Use the given information to write a linear function. f(x) = mx + b 5.) f(5) = 7 and f(3) = -5
6.) f(6) = 1 and f(0) = -5
7.)
8.)
Objective #5: Can you write the equation of a line in Slope-Intercept form? Write an equation for each line below. a.) passes through (-4, -3) with a slope of 3.
8|Page
b.) passes through (4, 2) and (0, -8)
Use the given table of values to write a linear equation or function for the given values.
7)
x
y
-1
8)
x
f(x)
-5
-1
5
0
-3
3
-3
1
-1
7
-11
Reflection #3 Describe in your own words the process to write an equation of a line in slopeintercept form when you use the point-slope formula.
Word Problem: During the 2000 census the population of Reno was 180,000. By the 2010 census the population of Reno had grown to 225,000. Assuming that the population grew at a constant rate: a.) Write an equation in slope-intercept form that represents the population of Reno since 2000?
b.) Use the equation above to approximate the population of Reno in 2005 to the nearest thousand?
Objective #6: Can you solve word problems using equations of lines? Solve the following problem. At the beginning of the year Josh had $150 in his savings account. After 6 Months he had $360. Assuming that he deposited the same amount each month: a.) Write and equation in slope intercept form that shows how much money is in Josh’s account, x months after the beginning of the year.
b.) If Josh continues to deposit the same amount each month, how much money will be in Josh’s account after 10 months? 9|Page
4.3 Parallel and Perpendicular Slopes and equations: How can you write equations of parallel and perpendicular lines?
Warm-Up: 1. Identify the property illustrated in each equation. a. 𝟐𝒙 𝟑 𝟑 𝟐𝒙 b. 𝟓(𝟐𝒙 𝟑) 𝟏𝟎𝒙 𝟏𝟓
c. 𝟒 (𝟓 𝟔𝒙) (𝟒 d. 𝟏𝟐𝒙 𝟎 𝟏𝟐𝒙
𝟓)
𝟔𝒙
2. Write an equation for a line given the following info: a. 𝐩𝐚𝐬𝐬𝐞𝐬 𝐭𝐡𝐫𝐨𝐮𝐠𝐡 (𝟏 𝟑)𝐰𝐢𝐭𝐡 𝐚 𝐬𝐥𝐨𝐩𝐞 𝐨𝐟 𝟐. b. passes through (4, 2) and (0, -8)
Parallel, Perpendicular, or Neither: Parallel – Two lines are said to be parallel if they have the _____________
_______________.
If two lines are not parallel, they have to _________________________ at some point. Perpendicular – Two lines that intersect at a ___________ ___________ are perpendicular. For two lines to be perpendicular, their _________ must be ________________ _________________. Neither – If two lines are not __________________ or _________________, they are said to be neither.
Parallel:
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Perpendicular:
Neither:
Determine whether the given slopes would result in lines that are parallel, perpendicular or neither. 1.
and
2.
and
3.
and -4
4.
Objective #7: Can you decide of lines are parallel, perpendicular, or neither by comparing slopes? a)
and
b) -4 and
c) 1 and -1
Determine whether the two given lines are parallel, perpendicular or neither by looking at their slopes. (
1.
) and
2.
Example 1: Write the equation form.)
Example 2: Determine if neither.
and
as a function for y in terms of x (slope-intercept
and
are parallel, perpendicular, or
Hint: Re-write each equation in slope-intercept form (solve for y).
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*Examples: Rewrite the equations below in slope intercept form. 1.
2.
3.
4.
5. Which equation represents a line that is parallel to the line for equation number 2?
6. Name two equations that represent perpendicular lines.
7. Are the lines represented by the equations in number 2 and number 3 parallel, perpendicular, or neither?
Objective #8: Can you decide if lines are parallel, perpendicular, or neither when given equations? a)
and
c)
and
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b)
and
Reflection #4 How do you know when lines are parallel, perpendicular or neither?
Parallel vs. Perpendicular Parallel:
Perpendicular:
Example 1: Write an equation of a parallel line. Write an equation of the line that passes through (2, 3) and is parallel to the line y = 4x + 1.
*Examples: Write an equation of the line that is parallel to the given line and passes through the given point. 1.
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; (10, 1)
2.
; (-6, 5)
Objective #9: Can you write an equation of a line that is parallel to a given line, passing through a given point? a. (5, 3), y = 6x + 1
b. (10, –8),
Example 1: Write an equation of a perpendicular line. Write an equation of the line that passes through (-2, 4) and is perpendicular to the line
.
*Examples: Write an equation of the line that is perpendicular to the given line and passes through the given point.
1.
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; (10, 1)
2.
; (-6, 5)
Objective #10: Can you write an equation of a line that is perpendicular to a given line, passing through a given point? a. (3, 7), y =
1 x +1 5
b. ( –6, 2), y = 2x + 6
Reflection #5 Compare and contrast the process to write linear equations that are parallel or perpendicular to a given line and passing through a given point.
4.4 Notes: Correlation and Lines of best fit How can you decide whether a correlation exists between paired numberical data?
Warm-Up: #1-2 Use the following information: Write an equation in slope-intercept form that is parallel to the given equation and contains the given point.
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(
)
Write an equation in slope-intercept form that is perpendicular to the given equation and contains the given point.
Correlation involves a graph of paired data points called a _____________________. A scatterplot is just a graph of a bunch of points or ordered pairs.
Scatterplots compare ___________________ different variables on the same graph. For the scatter plot to the left, each dot represents one person’s ________________ and ________________.
Scatterplots can have different types of __________________ that describe relationships between variables. _______________ Correlation
________________ Correlation
_____ Correlation
A line of _____________ _____________ can be used to help describe the patterns in a scatterplot, and allow predictions to be made.
Draw a line of best fit in the graphs above for positive and negative correlation. This is not a dot-to-dot! Keep your line _________________________. Try to get half of the points ______________ your line, and around half of the points _______________ your line.
The ___________________ __________________, denoted by the letter ____, is a measure of the strength of the linear relationship between two variables. The correlation coefficient takes on values ranging from ____ to _____. A correlation coefficient of -1 means the points form a _______________ line with negative corrleation. A correlation coefficient of 1 means that the points form a straight line with a positive correlation.
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Example: Match the value of r to each scatterplot. Choices for r: -1, -.8, 0, 0.8, 1
Reflection #6 How is the correlation coefficient similar to slope?
Objective 11: Can you match a r value to a scatterplot? Use the following r values and match them with the given scatter plots. Choices for r: -.6, 0, .8
Example: A. B. C. D.
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Which linear equation approximates the best fit to the data?
Example: The table below shows the average attendance at a school's varsity basketball games for various years. Year
2000
2001
2002
2003
2004
2005
2006
Avg. Game Attendance
488
497
525
567
583
621
688
1) Make a scatterplot of the data.
2) Draw in a line of best fit.
3) Use your line of best fit to make a prediction about the average attendance in 2007.
Objective #12: Can you describe the correlation of a scatter plot? a) b) c) 25
30
25
25
20
20 20
15
15 15
10
10
10
5
5
5 0
0
0 0
5
10
15
0
Objective #13: Can you use a scatter plot to estimate values? a) Using the scatter plot shown, what would you expect the temperature in Nevada to be at 2500 meters elevation?
b) At around what elevation would you expect the temperature to be 15 degrees Celsius?
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5
10
15
0
5
10
15
