NOTESNOTES Many relations in business and science Many relations in business and science

are linear.are linear.

The slope and intercepts of the graphs of The slope and intercepts of the graphs of these relations represent different these relations represent different things.things.

Variables other than “x” and “y” may be Variables other than “x” and “y” may be used.used.

DEPENDENT VERSES DEPENDENT VERSES INDEPENDENTINDEPENDENT

Dependent VariableDependent Variable : the output of a : the output of a relation; often denoted “y”relation; often denoted “y”

Independent VariableIndependent Variable: the input of a : the input of a relation; often denoted “x”relation; often denoted “x”

When graphing variables other than “x” and When graphing variables other than “x” and “y”, plot the “y”, plot the dependent variable verticallydependent variable vertically..

Plot the Plot the independent variable horizontallyindependent variable horizontally..

Dependent VariableDependent Variable: the : the output of a relation; often output of a relation; often denoted “y”denoted “y”

Independent Independent VariableVariable: the input of : the input of a relation; often a relation; often denoted “x”denoted “x”

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 - ap = 220 - a, where pp is the number of beats per minute and aa is your age in years.

a) Make a table of values for the equation p = 220 - a, for ages between 18 and 50.

b) Graph pp against aa.

c) Find the slope of the line. What does the slope represent?

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)When a = 18, p = 220 - (18)

= 202= 202

When a = 25, p = 220 - (25)When a = 25, p = 220 - (25)

=195=195

When a = 40, p = 220 - (40)When a = 40, p = 220 - (40)

= 180= 180

When a = 50, p = 220 - (50)When a = 50, p = 220 - (50) = 170= 170

Age,a(years)Age,a(years)Maximum Maximum pulse, p pulse, p

(beats/min)(beats/min)

1818 202202

2525 195195

4040 180180

5050 170170

B) Graph the relation.

Plot the data from the table. Since the variable p is used instead of y, plot p vertically.

c) Find the slope of the line. What does the slope c) Find the slope of the line. What does the slope represent?represent?

The graph is a straight line. Choose any 2 points on the line, such as A(40, 180) and B(50,170).

Slope =Slope = RISERUN

== 170-180 50-40

-10 10

==

== -1-1

The slope of the line is -1The 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.

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