Daily Problem for Tuesday 10/11/16

3.1 Representing Proportional Relationships Essential Question: Page 71 How can you use tables, graphs, & equations to represent proportional situations?

Materials needed Textbook Pencil Highlighter(s) Calculator Whiteboard/marker

Colin Berg, Expert Fry-man

Proportional Relationship a relationship between two quantities (numbers) in which the ratio (division) of one quantity (output) to the other quantity (input) is constant page 72 Example: Colin works at Wendy’s for 8 hours (input) on Sunday and earns $72 (output). He works on Tuesday for 5 hours (input) and earns $45 (output). This represents a proportional relationship because $72/8hrs = $9.00 per hour and $45/5hrs = $9.00 per hour

Constant of Proportionality (k) In a proportional relationship, when the output (y) is divided by the input (x) the result is known as the constant of proportionality (k) page 72 Example: Colin’s hourly rate ($9.00 per hour) is the constant of proportionality (k) The equation y ÷ x = k can be used to find the C of P (k) Once the C of P is found, it can be used to find the output for any input using the equation y = kx

Example 1, page 72 Number of hrs 1 2 4 8 Amount earned 12 24 48 96 To find k, divide the amount earned (output) by the number of hours (input) 12÷1=12 24÷2=12 48÷4=12 96÷8=12 k=12 To find amount earned for any # of hours, use the equation y=12x

Your Turn page 72

Representing Proportional Relationships with Graphs page 73 A Proportional Relationship on a graph must: Be a straight line Pass through the origin (0,0) What is the C of P? Time (x) 2 4 6 8 10 Miles (y) 92 184 276 368 460

Your Turn page 73

Textbook Assignment #1-6 page 74 Answers in Selected Answers page SA3

Worksheet Assignment