Question

practice

1. find the pattern and then write a rule and an equation that represents the pattern. then complete the table.

x	0	2	10	16	20
y	0	1	5

1. use the equation to complete the table.

$y = 6x + 1$

x	1	2	3	4	5
y

Explanation:

Step1: Analyze Problem 1 Pattern

Check ratios of \( y \) to \( x \): \( \frac{0}{0}=0 \), \( \frac{1}{2}=0.5 \), \( \frac{5}{10}=0.5 \). So rule: \( y=\frac{1}{2}x \) (or \( y = 0.5x \)).

Step2: Calculate \( y \) for \( x = 16 \)

Substitute \( x = 16 \) into \( y=\frac{1}{2}x \): \( y=\frac{1}{2}\times16 = 8 \).

Step3: Calculate \( y \) for \( x = 20 \)

Substitute \( x = 20 \) into \( y=\frac{1}{2}x \): \( y=\frac{1}{2}\times20 = 10 \).

Step4: Analyze Problem 2 Equation

Given \( y = 6x + 1 \), substitute \( x \) values:

• \( x = 1 \): \( y = 6(1)+1 = 7 \)
• \( x = 2 \): \( y = 6(2)+1 = 13 \)
• \( x = 3 \): \( y = 6(3)+1 = 19 \)
• \( x = 4 \): \( y = 6(4)+1 = 25 \)
• \( x = 5 \): \( y = 6(5)+1 = 31 \)

Answer:

Problem 1 Table Completion:

For \( x = 16 \), \( y = 8 \); for \( x = 20 \), \( y = 10 \).

Problem 2 Table Completion:

For \( x = 1 \), \( y = 7 \); \( x = 2 \), \( y = 13 \); \( x = 3 \), \( y = 19 \); \( x = 4 \), \( y = 25 \); \( x = 5 \), \( y = 31 \).