Two-Variable Data: Tables, Graphs, and Patterns Worksheet

Question 1

The table shows the cost of notebooks at a school store. 1 notebook costs $2, 2 notebooks cost $4, 3 notebooks cost $6, and 4 notebooks cost $8. What is the rule relating the number of notebooks, n, to the cost, c?

Accepted Answer

The rule is c = 2n. Each notebook costs $2, so the total cost is 2 times the number of notebooks.

Question 2

A taxi charges a starting fee of $5 plus $3 for each mile. Complete the table for 0, 1, 2, 3, and 4 miles, then write an equation for the total cost, c, in dollars after m miles.

Accepted Answer

The completed table is 0 miles: $5, 1 mile: $8, 2 miles: $11, 3 miles: $14, and 4 miles: $17. The equation is c = 3m + 5 because the cost increases by $3 per mile and starts at $5.

Question 3

The points (1, 4), (2, 7), (3, 10), and (4, 13) follow a pattern. What is the change in y for each increase of 1 in x? Write an equation for the relationship.

Accepted Answer

The y-value increases by 3 each time x increases by 1. The equation is y = 3x + 1.

Question 4

A graph of a relationship contains the points (0, 2), (1, 5), (2, 8), and (3, 11). What is the y-intercept, and what does it mean in this relationship?

Accepted Answer

The y-intercept is 2 because the graph crosses the y-axis at (0, 2). It means that when x is 0, the value of y is 2.

Question 5

The table shows the number of cups of flour needed for batches of muffins: 1 batch needs 2 cups, 2 batches need 4 cups, 3 batches need 6 cups, and 4 batches need 8 cups. Is this a proportional relationship? Explain.

Accepted Answer

Yes, this is a proportional relationship because the ratio of cups of flour to batches is always 2 to 1. The equation is y = 2x, and the graph would pass through the origin.

Question 6

A gym charges a one-time sign-up fee of $20 plus $10 per month. Is the relationship between months and total cost proportional? Explain.

Accepted Answer

No, the relationship is not proportional because there is a $20 starting cost when the number of months is 0. A proportional relationship must have the form y = kx and pass through the origin.

Question 7

The ordered pairs (2, 6), (4, 12), (6, 18), and (8, 24) are graphed. Describe the pattern and write the equation.

Accepted Answer

The y-value is always 3 times the x-value, so the pattern is multiplication by 3. The equation is y = 3x.

Question 8

A plant is 6 centimeters tall when it is measured on day 0. It grows 2 centimeters each day. Make a table for days 0 through 5 and write an equation for the height, h, after d days.

Accepted Answer

The table is day 0: 6 cm, day 1: 8 cm, day 2: 10 cm, day 3: 12 cm, day 4: 14 cm, and day 5: 16 cm. The equation is h = 2d + 6.

Question 9

A student says the relationship in the table x: 1, 2, 3, 4 and y: 2, 4, 8, 16 is linear because y increases each time. Is the student correct? Explain.

Accepted Answer

The student is not correct. The relationship is not linear because the y-values do not increase by the same amount each time. The increases are 2, 4, and 8.

Question 10

The scatter plot shows hours studied and quiz scores for 10 students. The points generally rise from left to right. What type of association does the scatter plot show, and what does it mean?

Accepted Answer

The scatter plot shows a positive association. This means that students who studied more hours tended to have higher quiz scores.

Question 11

The scatter plot shows the age of a used car and its selling price. The points generally fall from left to right. What type of association does the scatter plot show, and what does it mean?

Accepted Answer

The scatter plot shows a negative association. This means that older used cars tended to have lower selling prices.

Question 12

For the equation y = 4x - 3, find the y-values when x = 0, 1, 2, and 3. Then describe the pattern.

Accepted Answer

The y-values are -3, 1, 5, and 9. The pattern is that y increases by 4 each time x increases by 1.

Question 13

A line goes through the points (3, 9) and (7, 17). What is the rate of change of y with respect to x?

Accepted Answer

The rate of change is 2. The change in y is 17 - 9 = 8, and the change in x is 7 - 3 = 4, so 8 divided by 4 equals 2.

Question 14

A movie rental service charges $4 per movie plus a monthly membership fee. The table shows that 2 movies cost $14 and 5 movies cost $26. What is the monthly membership fee?

Accepted Answer

The monthly membership fee is $6. Since each movie costs $4, 2 movies cost $8, and $14 - $8 = $6.

Question 15

A graph shows the relationship between time and distance for a bicyclist. The line starts at (0, 0) and passes through (2, 18) and (4, 36). What is the bicyclist's speed in miles per hour?

Accepted Answer

The bicyclist's speed is 9 miles per hour. The distance increases by 18 miles in 2 hours, and 18 divided by 2 equals 9.

Two-Variable Data: Tables, Graphs, and Patterns

Related Cheat Sheets

More Math Worksheets

More Grade 6-8 Worksheets