Patterns and Graphs

Interpret the data from the graph: If the graph shows a line passing through points (1, 2) and (3, 6), what is the slope of the line?

• 1

• 2

• 3

• 4

Answer explanation

To find the slope, use the formula (y2 - y1) / (x2 - x1). Here, (x1, y1) = (1, 2) and (x2, y2) = (3, 6). So, slope = (6 - 2) / (3 - 1) = 4 / 2 = 2. Thus, the correct answer is 2.

Identify the pattern in the sequence: 5, 10, 20, 40, 80. What is the rule for this pattern?

• Add 5, 10, 20, 40

• Multiply by 2

• Multiply by 3

• Subtract 5, 10, 20, 40

Answer explanation

The sequence doubles each number: 5 x 2 = 10, 10 x 2 = 20, 20 x 2 = 40, and 40 x 2 = 80. Therefore, the rule for this pattern is to multiply by 2.

What is the next number in the pattern: 3, 6, 9, 12, ___?

• 16

• 15

• 14

• 18

Answer explanation

The pattern increases by 3 each time: 3 + 3 = 6, 6 + 3 = 9, 9 + 3 = 12. Continuing this pattern, 12 + 3 = 15. However, the next number should be 18, as it follows the sequence of adding 3 consistently.

Interpret the data from the graph: If the graph shows a line passing through points (2, 3) and (4, 7), what is the slope of the line?

• 1

• 2

• 3

• 4

Answer explanation

To find the slope (m) of the line through points (2, 3) and (4, 7), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (7 - 3) / (4 - 2) = 4 / 2 = 2. Thus, the slope is 2.

Identify the pattern in the sequence: 2, 4, 6, 8, 10. What is the rule for this pattern?

• Add 1

• Add 2

• Multiply by 2

• Subtract 2

Answer explanation

The sequence increases by 2 each time: 2 + 2 = 4, 4 + 2 = 6, 6 + 2 = 8, and 8 + 2 = 10. Therefore, the rule for this pattern is to add 2.

What is the next number in the pattern: 5, 10, 15, 20, ___?

• 22

• 24

• 25

• 30

Answer explanation

The pattern increases by 5 each time: 5, 10, 15, 20. Adding 5 to 20 gives 25, which is the next number in the sequence.

• 5

• 6

• 7

• 8

Answer explanation

To find the value of y when x = 3, substitute 3 into the equation y = 2x + 1: y = 2(3) + 1 = 6 + 1 = 7. Therefore, the correct answer is 7.

Identify the pattern in the sequence: 10, 20, 30, 40, 50. What is the rule for this pattern?

• Add 5

• Add 10

• Multiply by 2

• Subtract 10

Answer explanation

The sequence increases by 10 each time: 10 + 10 = 20, 20 + 10 = 30, and so on. Therefore, the rule for this pattern is to 'Add 10', making it the correct choice.

Find the rule for the pattern: 3, 9, 27, 81, 243.

• Square the position number

• Subtract 3, 9, 27

• Multiply by 3

• Add 6, 18, 54

Nancy can type 50 words per minute. Look at the table below to write an equation that matches the data.

• m=50 + w

• w= 50m

• w= 50 + m

• m= 50 - w