Representing Linear Patterns Section 1.5

A DVD buyers club charges a $20 membership fee and $15 per DVD purchased. The table below represents this situation. Number of DVDs purchased d 1 2 3 4 5 Total cost ($) c 20 35 50 65 80 95 +15 +15 +15 +15 +15 Find the first differences for the total cost. constant linear Since the data shows a ___________ difference the pattern is __________. If a pattern is linear then its graph is a straight _________. line

This is called a linear equation. Number of DVDs purchased d 1 2 3 4 5 Total cost ($) c 20 35 50 65 80 95 The equation represents this situation. This is called a linear equation. 80 70 Constant difference or price per DVD Membership fee 60 50 40 30 20 10 1 2 3 4 5

Number of CDs purchased Example 1: The costs associated with being a member of a CD Club are presented in the table below. Find the first differences and write an equation to represent the data pattern. Number of CDs purchased n 1 2 3 4 5 Total cost ($) c 26 39 52 65 78 91 +13 +13 +13 +13 +13 $13 The club charges _________ per CD. The cost for 0 CDs is ____________. Therefore, the club membership (initial cost) must be _________. $26 $26

Try this… The table shows the costs associated with being a member of a DVD club that charges a membership fee. Write an equation to represent the pattern in the data. Number of DVDs purchased n 1 2 3 4 5 Total cost ($) c 21 31 41 51 61 71 +10

Remember from Example 1: n represented the number of CDs purchased and c represented the total cost Linear equations contain an independent variable and a dependent variable. independent dependent In this case n is called the ________________ variable and c is called the ________________________ variable. The total cost (c) depends on the number of CD purchased (n).

dependent independent On a graph, the independent variable is on the ________________ axis and dependent variable is on the _______________ axis. horizontal vertical dependent independent

time t Distance Rate Time Example 2: A jet airplane is flying at a rate of 280 miles per hour. Write a linear equation to express the distance traveled in a given amount of time. Graph the equation for times from 0 to 10 hours. The distance traveled can be represented by __________________ = ________________ x _______________ Distance Rate Time To find the ordered pairs (points) for the graph, make a table. Since distance depends on time, ________________ is the independent variable, and you can choose values for ___. time t

Linear Equation: Time (hours) t 2 4 6 8 10 Distance (miles) d 560 1120 1680 2240 2800 3000 2700 2400 2100 1800 1500 1200 900 600 300 2 4 6 8 10

Example 3: Exercise physiologists suggest that a reasonable estimate for the maximum heart rate during exercise is no more than 220 beats per minute minus the person’s age. Represent the maximum heart rate by r and the age by a. Write a linear equation to express the maximum heart rate (r) , in terms of age (a). Create a table for ages from 10 to 50. Rate equals 220 beats minus the person’s age - r = a 220 age Since the ________ depends on the ______, then ______ is the independent variable. You can choose values for _________. rate age age

age (years) a Maximum heart rate r 10 20 25 30 40 50 210 200 195 190 180 170