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Creating Equations, Tables, and Graphs from Verbal Representations

In this lesson, students will learn how to translate verbal representations into mathematical equations, tables, and graphs. By reviewing the slope-intercept form of a linear equation (y = mx + b), students will understand key concepts such as rate of change (slope) and initial value (y-intercept). Through multiple examples, including real-life scenarios like growth in animal populations and budgeting for movie rentals, students will practice constructing numeric and algebraic functions. They will also have homework problems to further enhance their skills in this area.

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Creating Equations, Tables, and Graphs from Verbal Representations

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  1. 2.5B Create an Equation, Table and Graph

  2. In this lesson you will create an equation, table, and graph from a verbal representation

  3. Let’s Review Slope-intercept form: y = mx + b Slope (rate of change) y-intercept (initial value) y = -1.5x + 2

  4. Let’s Review A linear function has a constantrate of change (slope) and an initial value (y-intercept). 1 – 0 1 5 – 2 3 y = 3x + 2 31

  5. Example1: Create an equation, table, and graph from a verbal representation A wild animal park opens with 100 antelope and the population grows by 5 antelope every year. y-intercept Slope y = 100 + 5x

  6. Example 1- continued Construct (write) a numeric representation from the verbal representation. y = + x Y-intercept 1 – 0 105 - 100 5 1 5 1 Slope = =5 100 5

  7. Example 1 continued Construct (write) a algebraic function from the graphic representation. y = + x 10 10 y-intercept Slope = 5 2 2 5 100

  8. Example 2: Create an equation, table, and graph from a verbal representation. Joan’s aunt agreed to loan Joan $500 to buy a used car as long as Joan pays back $50 per month.

  9. Joan’s Aunt agrees to loan Joan $500 to buy a used car as long as Joan pays back $50 per month. slope = 50 Slope “indicator” y = 50x - 500 y-intercept = -500

  10. Joan’s Aunt agrees to loan Joan $500 to buy a used car as long as Joan pays back $50 per month. y-intercept 1 - 0 =1 slope 50= -450 - -500 0 -500 1 -450 2 -400 3 -350

  11. Joan’s Aunt agrees to loan Joan $500 to buy a used car as long as Joan pays back $50 per month.

  12. Practice Example 1: Linda begins the year with $200 in her bank account. Each month, she deposits $50. Create an equation, table, and graph from this verbal representation .

  13. Practice Example 2: • A parachutist is 500 feet above the ground. After she opens her parachute, she falls at a constant rate of 25 feet per second. • Create the equation, table, and graph for the scenario.

  14. Practice Example 3: Construct an algebraic equation using the graph provided below. 25 5

  15. Homework: Problems 1-9

  16. Homework Problem 1: • Construct an algebraic equation for each of the given representations. a 50 b 10 c • Multiply x by 0.6 and add 7

  17. Homework Problem 2: • Write an algebraic equation for this scenario. Make a table to help before you write it. • Parking Lot Prices Entrance fee . . . $3.00 • Each hour . . . $1.50

  18. Homework Problem 3 Jordan’s movie rental company charges a monthly fee of $5.00 plus an additional cost of $1.25 per movie rental. Which of these equations represents the total monthly cost (c) of renting (x) movies? C = 1.25x + 5.00 C = 3.75x + 5.00 C = 5.00x + 1.25 C = 5.00x + 3.75

  19. Homework Problem 4: Which is the graph of y = -3x + 5 ? b d a c

  20. Homework Problem 5 • Match each equation to its table. • y = -4x - 3 • y = -3x - 4 • y = -3 + 4x

  21. Homework Problem 6 A restaurant charges $160 for a room and $10 per person for food and drinks. Which table is correct for this situation? a b c d

  22. Homework Problem 7 :Another restaurant charges $150 for a room and $10 per person for food and drinks. Which is the correct graph? a b c d

  23. Homework Problem8: Thomas is 300 miles away from home. He drives 50 miles per hour. Create an equation, table, and graph to represent this situation.

  24. Homework Problem 9: • We had 15 inches of snow. It snowed at a rate of 5 inches per hour. • Create an equation, table, and graph for the scenario. 

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