Patterns in a Table of Values Chapter 6

Patterns in a Table of Values Chapter 6. 6

Patterns in a Table of Values Expression: a combination of letters and numbers and operations (+, -, x, ÷) Ex 2 b + 1 Variable: Ex. or 8 – 5 g or -10 x + 9 a letter that represents an unknown amount 3 a – 5 the variable is the a

Example 1 Table 1 x y 2 3 4 7 6 11 8 15 b) What is the pattern for each variable? Table 1 Table 2 m N 1 1 2 4 3 7 4 8 2 4 6 8 Graph of Table 1 Linear m = +1 N = No common pattern a) Graph the table of values y 16 14 12 10 8 6 4 2 0 Table 2 x = +2 y = +4 10 x Graph Straight line c) Which relations is linear? N 8 7 6 5 4 3 2 1 0 Not linear Graph 1 is linear. Graph 2 is not. 1 2 3 Graph of Table 2 4 5 m

Example 2 Find the expression for the following chart +1 a B 0 0 1 3 2 6 3 9 4 12 x 3 a) What is the difference in value in consecutive i) ii) a-values B-Values +1 +3 b) If linear, describe the relationship between a and B +3 Multiple by 3 c) What is the expression for B in terms of a ax 3 or 3 a

Example 3 Find the expression for the following chart x 1 2 3 4 5 6 7 y 5 10 15 20 25 30 35 a) What is the difference in value in consecutive i) ii) x-values +1 y-values +5 b) If linear, describe the relationship between x and y Multiply by 5 c) What is the expression for y in terms of x 5 • x “ • ” means multiply Or 5 x

Example 4 Photo world charges $3 for the first enlargement and $2 for each additional enlargement. What is the cost of 15 enlargements? a) Make a Table of Values b) Is this a linear relation? Yes # of photos n 1 2 3 4 Cost C 3 5 7 9 n = +1 C = +2 c) Write the expression for the cost in relation to the number of enlargements? 2 n check? not true 2 n + 1 d) What is the cost of 15 enlargements? C = 2 n + 1 C = 2(15) + 1 C = 31 Cost of 15 photos would be $31.

Example 5 - Sara sells magazine subscriptions. She receives $20 for every five subscription she sells. How much does she get for selling 40 subscriptions? s P • # of subscriptions 0 5 10 15 20 25 30 35 Pay $ 0 20 40 60 80 100 120 140

Example 6 Find the expression for the following chart Table 1 x y 2 3 4 7 6 11 8 15 +2 +4 Yes

• 9. 2 Patterns in a Table of Values – Practice Apply #7 -11