Chapter 6: Linear Equations & Their Graphs 6.1 Rate 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 variable Change 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 daysRental 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

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 even, all