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Example 1 For the data, is the rate of change for each pair of consecutive days the same? What does the rate of change represent? Cost of Renting a Computer # of daysRental Charge 1$60 2$75 3$90 4$105 5$120
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Chapter 6: Linear Equations & Their Graphs
6.1Rate of Change and Slope
Vocabulary
• Rate:– A comparison of two quantities measured in
different units• Rate of change:– Allows you to see the relationship between two
quantities that are changing
Change in the dependent variableChange in the independent variable
Example 1
• For the data, is the rate of change for each pair of consecutive days the same? What does the rate of change represent?
Cost of Renting a Computer
# of days Rental Charge
1 $60
2 $75
3 $90
4 $105
5 $120
Example 1a
• Does finding the rate of change for just one pair of days mean that the rate of change is the same for all data?
Rate of Change
• If data is linear, you can use a graph to find a rate of change
vertical change (change in dependent variable)Horizontal change (change in independent variable)
Example 2• The graph shows the altitude of an airplane as it
comes in for a landing. Find the rate of change. Explain what this rate of change means.
Example 2a
• Find the rate of change of the data in the graph:
Slope
• The rate of change of a line
• Think of the slope of roads, roofs, etc.
• Steeper slope = larger number
Example 3a
• Find the slope of the line:
Example 3b
• Find the slope of the line:
Slope
xy
xxyy
runrisem
12
12
Example 4
• Find the slope of the line through A(-2,1) and B(6,7).
Example 4a
• Find the slope of the line through C(2,5) and D(4,7).
Example 4b
• Find the slope of the line through P(-1,4) and Q(3,-2).
Example 4c
• Find the slope of the line through M(a,b) and N(c,d)
Example 5
• Find the slope of the line:
Example 5a
• Find the slope of the line:
Example 5b
• Find the slope of the line:
Example 5c
• Find the slope of the line:
Summary
• Positive Slope
• Negative Slope
• Zero Slope
• No Slope
Homework
• P. 312
• 2-26 even, 30-35 all