Unit 3: Writing Linear Equations

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1 Unit 3: Writing Linear Equations Name: SUCCESS CRITERIA FOR WRITING AN EQUATION IN SLOPE-INTERCEPT FORM (y = mx + b) SUCCESS CRITERIA FOR WRITING AN EQUATION IN STANDARD FORM (Ax + By = C) 1

2 Slope Intercept Form Explore Activity Ranking Number: Card Letter Reasons: Ranking Number: Card Letter Reasons: Ideas for what you could do to write the line in y=mx+b form. Ideas for what you could do to write the line in y=mx+b form. Ranking Number: Card Letter Reasons: Ranking Number: Card Letter Reasons: Ideas for what you could do to write the line in y=mx+b form. Ideas for what you could do to write the line in y=mx+b form. 2

3 Ranking Number: Card Letter Reasons: Ranking Number: Card Letter Reasons: Ideas for what you could do to write the line in y=mx+b form. Ideas for what you could do to write the line in y=mx+b form. Ranking Number: Card Letter Reasons: Ranking Number: Card Letter Reasons: Ideas for what you could do to write the line in y=mx+b form. Ideas for what you could do to write the line in y=mx+b form. 3

4 Write Linear Equations in Slope-Intercept Form Notes Slope Intercept form If you are asked to write an equation in slope intercept form, what are the two parts of the equation you need to identify? Writing an Equation of a Line in Slope-Intercept Form Example 1: Write an equation of the line with the given slope and y-intercept. a. Slope is 8 b. Slope is y-intercept is -5 y-intercept is Example 2: Write an equation of the line given a point and has the given slope m. a. (1, 2), m = 3 b. (6, 3), m = 2 Try: Write an equation of the line that passes through the given point and has the given slope m. c. (2, 2), m = 4 d. (6, 3), m = -2 4

5 Example 3: Write an equation of a line given two points a. (1, 2), (-1, -4) b. (2, -3), (-2, 1) Try: Write an equation of the line given two points. c. (3, 0), (2, -4) d. (1, 2), (-1, -4) Example 4: Write an equation for the linear function f with the given values in function form. a. f(0) = 4, f(2) = 12 b. f(0) = 3, f(3) = 15 5

6 Example 5: Write an equation of the line when given a graph. Example 6: Write an equation of a line when given a story problem A dance academy charges $20 to use the facility and $25 per hour of instruction. a. Write an equation that gives the total cost to learn dance at the academy as a function of hours of instruction. b. Find the total cost of 2 hours of dance instruction. 6

7 Try: YouTube Example a) You post a hilarious video on YouTube and the number of thumbs up increases at a constant rate each day. If you have 15 thumbs up on day 1 and 60 thumbs up on day 10, write an equation to represent the total number of thumbs up on any given day. Applying what you Learned a) Let s change the scenario. Now you have a tree that is 12 inches tall and grows at a rate of 5 inches per year. Write the equation in slope-intercept form. b) Using the information from part a, explain what each value represents in the ordered pair: (2, 22) c) You have a tree that is 20 inches tall and grows at a rate of 7 inches per year. Write the equation in slope-intercept form. d) From part c, predict how tall the tree will be in 3 years? How much time has passed when the tree is 5 feet tall? 7

8 Use Linear Equations in Slope-Intercept Form Notes Example 1: a) You and some friends are going to the Drake concert. All tickets are the same price. Ticketmaster adds a fixed fee to every order. The cost of a concert ticket is $50. If 5 tickets cost $265 dollars, how much would 10 tickets cost? b) Write an equation for the cost of any number of tickets. c) What does each of the given numbers represent in the equation? $50 $5 $265 d) How could you use these three values and y=mx+b to obtain the equation we wrote in part B? Example 2: a) Thanksgiving is almost here! Butterball.com says it takes 20 minutes per pound to cook a turkey, but your oven requires extra time (it s old!). If it takes 4 hours and 5 minutes to cook an 11 pound bird, how much extra time does your oven require? b) Write an equation for the time it takes to cook any size bird. c) What does each of the given numbers represent in the equation? d) How could you use these three values and y=mx+b to obtain the equation we wrote in part B? 8

9 Model Direct Variation Notes Direct Variation Constant of variation Example 1: You love to order your favorite decaf caramel mocha non-fat latte at Starbucks. You go to Starbuck s every school day to buy your favorite drink. Assuming you don t miss any school days, you end up spending $47.20 in a two-week period. a) What is the cost of your drink? b) Write an equation to represent the cost of any number of drinks. c) Use your equation to figure out how much your coffee would cost in a month with 20 school days. d) Use your equation to figure out how many cups of coffee you ve purchased if you spend $ Example 2: You go to Chipotle and get the Burrito Bowl each time. You go to Chipotle 19 times in a month and spend $ How much does each burrito bowl cost? Write the direct variation equation. Example 3: Given that y varies directly with x, Use the specified values to write a direct variation equation that relates x and y. a. x = 2, y = 4 b. x = 3, y = -10 c x = -8, y = -1 9

10 Linear Equations in Standard Form Explore Examples of Equations in Standard Form 1. 10x 30y = x 4y = x 15y = x + 28y = x + 100y = x + y = 7 7. x + 2y = 6 Non-Examples of Equations in Standard Form A. 1 2 x y 3 5 B. y 0.25x 1.3 C. 2 2y 5 x 5 D x y E. y 2x x + 10y = x + 2y = 14 F. 1 y 3 x 2 1. What does it mean for an equation to be written in standard form? 2. What could you do to the equations on the right to write them in standard form? 3. Each equation on the right pairs with at least one equation on the left. Match the equivalent equations. 4. Some of the equations on the left are equivalent to each other. Match the equivalent equations. 10

11 Write Linear Equations in Standard Form Notes Standard Form Example 1: Write two equations in standard form that are equivalent. a. -0.5x + 6y = Equation 1 Equation 2 Try: Write two equations in standard form that are equivalent x + 2y = 1 3 Equation 1 Equation 2 Example 2: Write an equation in standard form of the line that passes through the given point and has the given slope m. a. (4, 3), m = 7 b. (-15, - 4), m =

12 Example 3: Write an equation in standard form of the line that passes through the given two points. a. (2, 4), (6, -4) b. (7, -3), (4, 1) Try: Write an equation in standard form of the line that passes through the given points. 1. (3, -1), (2, -4) Example 4: Write an equation of the specified line given a graph. a. Line A b. Line b 12

13 Write Equations of Parallel and Perpendicular Lines Notes Example 1: Example 2: Graph the two equations on the coordinate plane. 2 y x y x 2 2 Graph the two equations on the coordinate plane. 1 y x 1 4 y 4x 2 What is the relationship between the lines that you graphed? What do you notice about the slopes of the lines? Write 2-3 sentences explaining the relationship and your observations about the slopes. Parallel Lines (REVIEW) If two nonvertical lines in the same plane have the same slope, then they are parallel. If two nonvertical lines in the same plane are parallel, then they have the same slope. 13

14 Example 3: Graph the line given and the coordinate point. Use the slope of the line graphed to help draw your new line. Your new line is parallel to the line given. Part 1: a. (2, 4), y = 4x + 1 b. (-4, 6), y = -3x + 2 Part 2: Write an equation of the line that passes through the given point and is parallel to the given line. Try without graphing the line: Write an equation of the line that passes through the given point and is parallel to the given line. 1. (-1, 2), y = -3x + 1 Perpendicular Lines Lines that intersect to form a right angle. If two nonvertical lines in the same plane have slopes that are, then the lines are perpendicular. If two nonvertical lines in the same plane are, then their slopes are opposite reciprocals. 14

15 Example 4: Write an equation of the line that passes through the given point and is perpendicular to the given line. Part 1: Graph the coordinate point and the line. Use our discussion of perpendicular slopes to draw your new line. a. (-3, 4), y = 1 3 x + 2 b. (2, 9), 4x + y = 3 Part 2: Write the equation of the line. Try without graphing the line: Write an equation of the line that passes through the given point and is perpendicular to the given line. 1. (0, 4), y = x + 2 Example 5: Determine which of the following lines, if any, are parallel or perpendicular Line a: 12x 3y = 3 Line b: y = 4x + 2 Line c: 4y + x = 8 15

MODELING LINEAR PATTERNS NOTES Fit a Line to Data Scatter Plots: Positive Correlation Negative Correlation Relatively No Correlation Independent and Dependent Variables: Example 1: The number of

16 MODELING LINEAR PATTERNS NOTES Fit a Line to Data Scatter Plots: Positive Correlation Negative Correlation Relatively No Correlation Independent and Dependent Variables: Example 1: The number of minutes spent driving and the miles you have left to your destination. Correlation = Independent = Dependent = Example 2: The size of your shoe and your favorite TV show. Correlation = Independent = Dependent = Example 3: Your grade point average and the number of hours you spend on Snapchat. Correlation = Independent = Dependent = Challenge: As the Ocean Levels fall the fish population decreases Correlation = Independent = Dependent = 16

Scores on Tests 85 77 75 75 80 65 Hours Spent Playing Video Games 6 7 9 5 8 10 a) Identify the independent and dependent variables.

17 Line of Best Fit: When data shows a positive or negative correlation, you can model the trend in the data using a. There should be approximately half the points and half the points Example 5: The table shows the number of hours students spent playing video games and the score they received on their tests. Scores on Tests Hours Spent Playing Video Games a) Identify the independent and dependent variables. Independent: Dependent: b) Label your axes and then make a scatter plot. c) Describe the correlation of the data: As the number of hours of playing video games d) Write the equation of the line of best fit. e) Explain the meaning of the y-intercept. f) Explain the meaning of the slope. g) Predict a reasonable test score for playing video games for 12 hours. h) If Brian received a 50 on his test, what is a reasonable number of hours he played video games for? 17

18 Example 6: This table shows pizza size (cheese only) compared to the cost for a few different pizza places. [Dominos, Pizza hut, Homemade Pizza Co] Size(in) Cost($) a) Identify the independent and dependent variables. Independent: Dependent: b) Label your axes and then make a scatter plot. c) Describe the correlation of the data: d) Write the equation of the line of best fit. e) Explain the meaning of the y-intercept. f) Explain the meaning of the slope. g) If you wanted to buy a 20 in pizza, what would the cost of the pizza be? h) If you spent $11.11, what size pizza did you buy? 18

19 Predict with Linear Models Notes Best-fitting line Interpolation Extrapolation Example 1: The table shows the number of hikers who have completed the Appalachian Trail from 1996 to Year Hikers Completing Trail a) Make a scatter plot of the data where x is the number of years since b) Find the equation that models the number of hikers completing the trail as a function of the number of years since c) Approximate the number of hikers who d) Predict the number of hikers to completed the entire trail in complete the entire trail in

Slope Intercept form. Complete the graph below and write the equation of the line. Then, answer questions a-d.

Slope Intercept form. Complete the graph below and write the equation of the line. Then, answer questions a-d. Chapter 5: Writing Linear Equations Name: Section 5.1: Write Linear Equations in Slope-Intercept Form Slope Intercept form Complete the graph below and write the equation of the line. Then, answer questions