Linear Relationships

The graph shows the relationship between the number of times a gear can rotate in a period of time. Which of the following statements is true?

• If the gear rotates 30 times, then it has been rotating for 1.5 minutes (90 seconds).

• The graph satisfies the equation y = 10x.

• If the machine rotates for 10 minutes, then it will make 250 rotations.

• The relationship is non-proportional.

Which of the following tables best represents the relationship between x and y in the below equation?

y = 0.5x + 7

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What is the constant of proportionality between the number of pages read and the number of hours spent reading?

• 45 pages per hour

• 90 pages per hour

• 135 pages per hour

• 270 pages per hour

If a line was drawn through the points, why would this line show a proportional relationship?

• It is not curved

• It is a vertical line

• It connects all the dots

• It goes through the origin

Does this graph show a proportional relationship?

• Yes, because it is linear

• Yes, because it is linear and goes through the origin.

• No, because it is not linear

• No, because it does not go through the origin.

What can you use to represent linear relationships?

• verbal descriptions

• equations

• graphs

• tables

• all of the above

Which line shows a proportional relationship between x and y?

• Line L

• Line M

A machine can make 14,400 screws in 8 hours. A second machine can make twice as many screws per hour. What is the constant of proportionality between the number of screws and the number of minutes for the second machine?

• 90 screws per minute

• 180 screws per minute

• 60 screws per minute

• 3,600 screws per minute

Jacob’s parents have allowed him to get a cell phone but he must pay his own cell phone bill. He pays a flat rate of $35 a month and 50¢ for every minute he talks on the phone. If c represents the total cost of the bill and m represents minutes talking on the phone, which equation best fits the situation?

• c = 5m + 35

• c = 3.5m + 50

• c = 0.5m + 35

• c = 35 + 100 + 0.5

A student spends the same amount each week for bus fare. In 5 weeks, he spends $115. Which equation shows this relationship? Let x = number of weeks.

• y = 3.22x

• y = 5x

• y = 23x

• y = 115x