Name: Assignments for Algebra 1 Unit 4: Linear Functions and Correlation Day Date Assignment (Due the next class meeting) Thursday 10/25/12 (A) Monday 10/29/12 (B) 4.1 Worksheet Tuesday 10/30/12 (A) Wednesday 10/31/12 (B) 4.2 Worksheet Thursday 11/01/12 (A) Friday 11/02/12 (B) 4.3 Worksheet Monday 11/05/12 (A) Wednesday 11/07/12 (B) 4.4 Worksheet Thursday 11/08/12 (A) Friday 11/09/12 (B) Unit 4 Practice Test Tuesday 11/13/12 (A) Wednesday 11/14/12 (B) 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.. 1 P a g e
4.1: Writing Linear Functions How can you represent a function or equation in slope intercept form? Warm-Up: 1) Find the slope through 2) Solve: The given points (-2,4) and (6,-2) 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 y = mx + b Substitute for m and for b. y = x + 2 P a g e
Examples: Writing equations of a line given slope and y-intercept. 1. Slope is 8; y-intercept is -5 Writing linear functions when given a slope and intercept Write the linear function f using the given 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 b) slope = ½, y-intercept = 0 c) slope = 1, y-intercept = 3 c) slope = -, y-intercept = -2 Reflection 1 What two things do you need to know to write an equation of a line? 3 P a g e
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. b.) Write a linear function for the line shown. 4 P a g e
Example: Writing equations of horizontal and vertical lines. 1) Write an equation for each line from the graph. Line A: 2) Write an equation for each line in the graph below. 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? 5 P a g e
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) when given a verbal description? Objective 4: Can you write a linear function in the form f(x) = mx + b 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. 6 P a g e
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 b.) 2x 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 ( formula. ( ) ) and the slope to substitute into the point-slope 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. 7 P a g e
*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. b.) passes through (4, 2) and (0, -8) 8 P a g e
Use the given table of values to write a linear equation or function for the given values. 7) x y 8) -1-5 0-3 1-1 x f(x) -1 5 3-3 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 P a g e
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 c. 4 (5 6x) (4 5) 6x b. 5(2x 3) 10x 15 d. 12x 0 12x 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: Perpendicular: Neither: 10 P a g e
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. and Example 1: Write the equation form.) as a function for y in terms of x (slope-intercept Example 2: Determine if and are parallel, perpendicular, or neither. Hint: Re-write each equation in slope-intercept form (solve for y). 11 P a g e
*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 b) and c) and 12 P a g e
Reflection #4 How do you know when lines are parallel, perpendicular or neither? Parallel: Parallel vs. Perpendicular 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. ; (10, 1) 2. ; (-6, 5) 13 P a g e
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. ; (10, 1) 2. ; (-6, 5) 14 P a g e
Objective #10: Can you write an equation of a line that is perpendicular to a given line, passing through a given point? 1 a. (3, 7), y = + 1 b. ( 6, 2), y = 2x + 6 5 x 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. Write an equation in slope-intercept form that is perpendicular to the given equation and contains the given point. 15 P a g e
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. 16 P a g e
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. Which linear equation approximates the best fit to the data? 17 P a g e
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) 30 c) 25 25 20 15 10 5 0 0 5 10 15 25 20 15 10 5 0 0 5 10 15 20 15 10 5 0 0 5 10 15 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? 18 P a g e