2. NOTES Many relations in business and science are linear. Many relations in business and science are linear. The slope and intercepts of the graphs of these relations represent different things. The slope and intercepts of the graphs of these relations represent different things. Variables other than “x” and “y” may be used. Variables other than “x” and “y” may be used.

3. DEPENDENT VERSES INDEPENDENT Dependent Variable : the output of a relation; often denoted “y” Dependent Variable : the output of a relation; often denoted “y” Independent Variable: the input of a relation; often denoted “x” Independent Variable: the input of a relation; often denoted “x” When graphing variables other than “x” and “y”, plot the dependent variable vertically. When graphing variables other than “x” and “y”, plot the dependent variable vertically. Plot the independent variable horizontally. Plot the independent variable horizontally.

4. Dependent Variable: the output of a relation; often denoted “y” Independent Variable: the input of a relation; often denoted “x”

5. p = 220 - a pa When you exercise, your pulse should not exceed a maximum rate. The relation between the maximum rate and your age is represented by the equation p = 220 - a, where p is the number of beats per minute and a is your age in years. a)Make a table of values for the equation p = 220 - a, for ages between 18 and 50. pa b)Graph p against a. c)Find the slope of the line. What does the slope represent?

6. A) Make a table of values for the relation. Substitute some values for “a” into the equation p = 220 - a. Calculate the corresponding values of p. When a = 18, p = 220 - (18) = 202 = 202 When a = 25, p = 220 - (25) =195 =195 When a = 40, p = 220 - (40) = 180 = 180 When a = 50, p = 220 - (50) = 170 = 170Age,a(years) Maximum pulse, p (beats/min) 18202 25195 40180 50170

7. B) Graph the relation. Plot the data from the table. Since the variable p is used instead of y, plot p vertically.

8. c) Find the slope of the line. What does the slope represent? The graph is a straight line. Choose any 2 points on the line, such as A(40, 180) and B(50,170). Slope = RISE RUN = 170-180 50-40 -10 10 = = The slope of the line is -1 The slope is negative. So, as age increases, the maximum pulse decreases. Since the slope is -1, for each year increase in age, the maximum pulse decreases by 1 beat/minute.

9. Class work Copy notes from slides Copy notes from slides Check solutions to Lesson 13 Check solutions to Lesson 13 Complete Worksheet Lesson 13(2) Complete Worksheet Lesson 13(2)