Linear Modeling and Logic Unit

4.2 Slope and Rate of Change

For each of the following graphs:

a) Find the slope of the line.

b) Find the unit rate of change and interpret it in context to the information in the graph.

  1. The graph is linear and is decreasing from left to right. The x-axis represents time in years and goes from 0 to 5 counting by 0.5. The y-axis represents the value of a washing machine in dollars and goes from 0 to 500 counting by 50. The two points that are marked on the graph are (0,500) and (5,0).

    Slope = __________

    m = -100

    Rate of Change = _________________________

    The value of the washing machine decreases by $100 per year.

  2. The graph is linear and is increasing from left to right. The x-axis represents miles driven over 150 miles and goes from 0 to 50 counting by 5. The y-axis represents the total cost in dollars and goes from 0 to 50 counting by 5. The two points that are marked on the graph are (10,34.50) and (35,40.50).

    Slope = __________

    m = 6/25 = 0.24

    Rate of Change = _________________________

    After 150 miles, the total cost increases by $0.24 per mile.

  3. The graph is linear and is increasing from left to right. The x-axis represents time in minutes and goes from 0 to 25 counting by 5. The y-axis represents the water level in centimeters and goes from 0 to 240 counting by 20. The two points that are marked on the graph are (2.5,130) and (20,220).

    Slope = __________

    m = 36/7

    Rate of Change = _________________________

    The water level increases by approximately 5.1 cm per minute.

  4. The graph is linear and is decreasing from left to right. The x-axis represents time in months and goes from 0 to 25 counting by 1. The y-axis represents money owed in dollars and goes from 0 to 1400 counting by 100. The three points that are marked on the graph are (0,1080), (6,810) and (24,0).

    Slope = __________

    m = -45

    Rate of Change = _________________________

    The money owed decreases by $45 per month.

  5. The graph is linear and is decreasing from left to right. The x-axis represents miles traveled and goes from 0 to 80 counting by 10. The y-axis represents gallons of gas in the tank and goes from 0 to 6 counting by 1. The two points that are marked on the graph are (0,4) and (40,2).

    Slope = __________

    m = -1/20

    Rate of Change = _________________________

    The amount of gas in the tank decreases by 0.05 gallons per mile driven.

  6. The graph is linear and is increasing from left to right. The x-axis represents time in weeks and goes from 0 to 9 counting by 1. The y-axis represents the amount of money saved in dollars and goes from 0 to 90 counting by 5. The two points that are marked on the graph are (0,30) and (5,55).

    Slope = __________

    m = 5

    Rate of Change = _________________________

    The amount of money saved increases by $5 per week.

  7. The graph is linear and is decreasing from left to right. The x-axis represents time in minutes and goes from 0 to 45 counting by 5. The y-axis represents the distance from home in miles and goes from 0 to 5 counting by 0.5. The three points that are marked on the graph are (0,4) and (20,3), and (40,2).

    Slope = __________

    m = -1/20

    Rate of Change = _________________________

    The distance from home decreases by 0.05 miles per minute.

  8. The graph is linear and is increasing from left to right. The x-axis represents the price before tax in dollars and goes from 0 to 9 counting by 1. The y-axis represents the price including tax in dollars and goes from 0 to 10 counting by 1. The two points that are marked on the graph are (2,2.26) and (7,7.91).

    Slope = __________

    m = 113/100

    Rate of Change = _________________________

    The price including the tax increases by $0.13 per dollar spent.

  9. Circle the letter of each graph that shows a rate of change equal to 1.

    1. The graph is linear and is increasing from left to right. Two points on the graph are (0,10) and (20,30).

      m = 1

    2. The graph is linear and is increasing from left to right. Two points on the graph are (4,0) and (8,2).

      m = 1/2

    3. The graph is linear and is increasing from left to right. Two points on the graph are (3,0) and (5,2).

      m = 1

    4. The graph is linear and is increasing from left to right. Two points on the graph are (2,0) and (8,6).

      m = 1

    5. The graph is linear and is increasing from left to right. Two points on the graph are (0,0) and (10,5).

      m = 1/2

    6. The graph is linear and is increasing from left to right. Two points on the graph are (0,0) and (4,10).

      m = 5/2

    7. The graph is linear and is increasing from left to right. Two points on the graph are (0,0) and (5,5).

      m = 1

    8. The graph is linear and is increasing from left to right. Two points on the graph are (0,0) and (100,200).

      m = 2

    9. The graph is linear and is increasing from left to right. Two points on the graph are (0,0) and (20,20).

      m = 1

    10. The graph is linear and is increasing from left to right. Two points on the graph are (0,0) and (6,3).

      m = 1/2

      11. The graphs whose slopes are equal to 1 are a, c, d, g and i.