Objectives Represent linear patterns with equations. 1.5 Representing Linear Patterns Objectives Represent linear patterns with equations. Represent linear equations with graphs. WHY? Many situations, like the cost of participation in a buyer’s club, follow linear patterns. Linear equations can help you calculate solutions for problems that involve these situations.

1.5 Representing Linear Patterns Glossary Terms linear equation – an equation that, when graphed, forms a straight line independent variable – the variable that is graphed on the x-axis and its value doesn’t depend on anything else dependent variable - the variable that is graphed on the y-axis and the value depends on the value of the other variable

A DVD buyers club charges a $20 membership fee and $15 per DVD purchased. The table below represents this situation. Number of DVDs Purchased 1 2 3 4 5 Total Cost ($) 20 35 50 65 80 95 15 15 15 15 15 Since the first differences are constant, the pattern is linear. Let c represent the cost and d represent the number of DVD’s bought. c = 15d + 20 represent the pattern Notice the number 15 in the equation is the same as the first differences, and represents the cost per DVD. The number 20 in the equation represents the initial cost to join the club.

The costs associated with being a member of a DVD club are presented in the table below. Find the first differences and write an equation to represent the data pattern. Number of DVD’s purchased 1 2 3 4 5 Total Cost ($) 26 39 52 65 78 91 13 13 13 13 13 The first differences are a constant 13. That means the cost per DVD is $13. The cost for 0 DVD’s is $26. Therefore, the cost for joining the club is $26. The formula is c = 13d + 26

Time (hours) t 2 5 10 Distance (miles) d 560 1400 2800 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 rate is 280 miles per hour. Let d represent the distance in miles and t represent the time in hours. The linear equation that represents the distance traveled is : d = 280 t Time (hours) t 2 5 10 Distance (miles) d 560 1400 2800

Time (hours) t 2 5 10 Distance (miles) d 560 1400 2800 2500 2000 1500 2 5 10 Distance (miles) d 560 1400 2800 2500 2000 1500 1000 500 2 4 6 8 10

Key Skills Write and graph linear equations representing problem situations. A small cheese pizza costs $8. Each additional topping costs $1. 1 1 1 1 Model equation c = n + 8. Plot points (n, c) from the table and draw a line through them. TOC

Assignment Page 34 – 36 # 8 – 36 even, 40 -46