Grade 10 Applied Math Unit 3: Linear Equations Lesson: Date: Completed Level Lesson 1: Coordinates Review Lesson 2: Constructing Tables and Sketching


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1 Grade 10 Applied Math Unit 3: Linear Equations Lesson: Date: Completed Level Lesson 1: Coordinates Review Lesson 2: Constructing Tables and Sketching Graphs Lesson 3: Interpreting Lines Lesson 4: Write Linear Equations by Using a Table of Values Lesson 5: Write Linear Equations by Translating Written Descriptions Lesson 6: Reviewing Key Concepts Reminiscing Old Relationship Key Concepts Lesson 7: More Initial Value and Slope Variables and Equations with Graphs Lesson 7: More Initial Value and Slope Slopes and Stuff Homework Lesson 7: More Initial Value and Slope Graphs, Slopes, Intercepts and Equations Check Lesson 8: Graphing from an Equation Can Graphing Get Any Easier? Lesson 8: Graphing from an Equation Rising and Running From a Point? Lesson 9: Conversions Temperature Conversions Lesson 9: Conversions Temperature Conversions  Practice Lesson 9: Conversions Modelling Algebraically Problems Lesson 9: Conversions Practice Models Lesson 10: Finding x and y intercepts Y and X Are you Intercepting Me? Lesson 10: Finding x and y intercepts Y and X Are you Intercepting Me Practice Lesson 10: Finding x and y intercepts Writing Equations of Lines Lesson 10: Finding x and y intercepts Jack and Jill Go up a Hill Lesson 10: Finding x and y intercepts Slopes A way Lesson 11: Writing Equations 3.8.4: Writing Equations of Lines Lesson 12: Writing Equations without Graphing 3.9.2: Yes, We got no Graph Paper! Lesson 13: Converting from Standard Form to Slope Yintercept form Practice Problems Lesson 13: Converting from Standard Form to Slope Yintercept form Converting from Standard to Slope YIntercept Form  Practice Lesson 14: Review Unit 3 Test
2 Unit 3: Lesson 1  Coordinates Review
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6 Unit 3: Lesson 2  Constructing Tables and Sketching Graphs Practice Problems Level 1: 1. For each table of values, find the missing values. a) b) c) d) 2. Complete each table of values. 3. Find two other points that would fit on the lines below. a) b)
7 Level 2: 4. Determine if the point satisfies the equation of the line. a) A(2, 1); y = 2x 5 b) B(3, 1); y = x + 2 c) C( 4, 3); y = 3x + 4 d) D( 2, 2); y = 4x A telephone carrier offers phone calls for 9 /min to Scotland. a) Write an equation relating the cost, c (in dollars), to the time, t (in minutes). b) Develop a table of values for each minute up to 8 min of phone calls to Scotland. c) Graph the relation on a Cartesian plane
8 Level 3: 6. A hardware store offers its customers 5 in coupons for every dollar spent in its store. The equation relating money spent, m (in dollars), to value of coupons, c(in dollars), is c=0.05m a) Develop a table up to $100 in purchases for the b) Graph the results of your table hardware store. Use mvalues of 0, 25, 50, 75, 100. c) Explain how the value of coupons received for $0, $75, and $100 compares to the value of coupons received for $25 d) Use your graph or table of values to determine the value of the coupons that you would receive for $175 in purchases.
9 Level 4: 7. Paramount Canada s Wonderland offers group discounted pricing as shown in the table. A group consists of a minimum of 25 people. The total group cost, c (in dollars), is found by multiplying the season price by the number of people, p, in the group. a) Write an equation to represent the total group cost for each season priced ticket. Then develop tables of values for all three seasons. Use a minimum of five pvalues for each table. b) Graph the 3 lines on the same set of axes. c) How much money would a group of 25 people save by choosing to go to Paramount Canada s Wonderland during the fall instead of the summer?
10 Unit 3: Lesson 3  Interpreting Lines Practice Problems Level 1: 1. Use points A and B to determine the slope in each diagram. 2. Find the slope of the line that passes through each pair of points. a) (4, 5) and (8, 11) b) ( 3, 4) and ( 5, 6) 3. State the slope and yintercept for each linear equation. a) y = 3x + 4 b) y = 2x 3 c) + 1 d) y = 0.5x 2
11 Level 2: 4. Determine the slope of the roof. 5. The graph shows the increase in the price of admission over a 4year period. Change the scales on the axes in two different ways. Describe how the increase in the price of admission appears in each of your graphs. Level 3: 6. For safety reasons, it is recommended that a wheelchair ramp be built with a 1 m rise and a 12 m run. a) What is the slope of the ramp? b) If the rise is only 65 cm, what will the run be using the slope from part a)? 7. If a hill has a grade of 6%, this means that for every 100m of horizontal change, there is a vertical change of 6m. If a road has a 6% grade, what is the vertical change, in metres, when the horizontal change is 4km?
12 Unit 3: Lesson 4  Write Linear Equations by using a table of values Practice Problems Level 1: 1. Determine the slope and yintercept for the graph of each line. a) b) 2. Find an equation in the form y = mx + b for the straight line represented by each table of values. a) b) 3. Determine the equation of a line given its slope, m, and yintercept, b. a) m = 3, b = 4 b) m = 2, b = 3 c) m = 5, b = 6 d)
13 Level 2: 4. Graph the line represented by each table. Label the line with its equation. a) b) For the ramp below, write an equation in the form y = mx + b. Level 3: 6. BZB Parking charges $3.00 for 1 h of parking, $4.50 for 1.5 h of parking, and $6.00 for 2 h of parking. a) Write an equation that represents this relationship. Define your variables. b) What do the slope and yintercept represent? c) Use the equation from part a) to predict the cost of 4 h of parking.
14 7. At Super Suds Car Wash 4 minutes of service will cost $2.00, 7 min cost $3.50, and ten minutes cost $5.00. a) Write an equation that represents this relationship. Define your variables. b) What is the cost per minute? c) What is the yintercept? Explain what this means? Level 4: 8. CarpetsRUs charges a standard fee plus an hourly rate for every job they are contracted to do. They charge $60 for a 1h job, $100 for a 2h job, and $140 for a 3h job. a) Write an equation that represents this relationship. Define your variables. b) What doe the slope and yintercept represent? c) Use the equation from part a) to predict the charge for a 5h job.
15 9. a) Find an equation for the straight line represented in each table of values. Comment on the relationship between the slopes of the lines. x x y y b) Graph both lines on the same set of axes. c) What is the geometric relationship between the graphs of these lines? d) Write a pair of equations whose graphs have this same relationship.
What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.
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