Select the correct table that describes the area of a rectangular garden that is 12 square feet and decide whether or not it is an inverse variation.

  1. No,
    Length (feet) Height (feet)
    3 9
    4 8
    5 7
    Incorrect. The formula for the area of a rectangle is A = l(w). The table is not a representation for this formula.
  2. Yes,
    Length (feet) Height (feet)
    1 12
    2 6
    3 4
    Correct! The table shows possible values for the length and width of a rectangle with an area of 12 sq feet. If the length and width are multiplied together the product is 12, the area of the rectangle.
  3. No,
    Length (feet) Height (feet)
    3 9
    4 8
    5 7
    Incorrect. The table shows possible values for the length and width for the area of a rectangle. If the length and width are multiplied together, the product is 12 sq feet, the area of the rectangle. The table is correct and is an example of an inverse variation.
  4. Yes,
    Length (feet) Height (feet)
    3 9
    4 8
    5 7
    Incorrect. The formula for the area of a rectangle is A = l(w). The table is not a representation for this formula.
QUESTION 2

Jose and Jorge were observing go carts racing around a track. They decided to collect data about the go carts while they were observing them. Below is a chart listing their information.

Rate (mph) Time (minutes)
2 15
3 10
5 6
6 5

Decide if the table represents an inverse variation relationship. If it does, determine the constant of variation.

A. No, it is not an inverse variation.
Incorrect. Multiply the rate times the time to see if the products are constant.

B. Yes, it is an inverse variation, and the constant of variation is 5.
Incorrect. The table represents an inverse function. The constant is found by multiplying the rate times the time. The product is 30 miles.

C. Yes, it is an inverse variation, and the constant of variation is 7.5.
Incorrect. An inverse variation is a relationship where the product of each pair of corresponding numbers is constant.

D. Yes, it is an inverse variation, and the constant of variation is 30.
Correct! The product of the rate times the time, d = rt, for each value is 30 miles, the constant.

QUESTION 3

Shari and Ali are good friends and like to go to each other's homes. Since Ali is on the track team she likes to time herself each time she goes to or from Shari's house. Ali uses the distance formula, d = rt, to calculate her rate. Below is the table Ali created.

Rate
(kilometers per hour) 		Time
(hours)
6 0.5
3 1
2 1.5

Decide whether or not if the table represents an inverse variation. If it does, find the constant of variation.

A. Yes, the constant of variation is 3.
Correct!

B. Yes, the constant of variation is 2.
Incorrect. For an inverse variation, the product of each pair of corresponding numbers is constant.

C. No, there is no constant of variation.
Incorrect. For an inverse variation, the product of each pair of corresponding numbers is constant.

D. Yes, the constant of variation is 12.
Incorrect. For an inverse variation, the product of each pair of corresponding numbers is constant.

QUESTION 4

Everyone in Ms. Gomez's class was asked to bring in one type of fruit. Kim decided to make a table of the three types of fruit she was considering. Decide if the table Kim created is an inverse variation, and if so, the amount of money Kim has to spend purchasing her fruit.

Item Number of pounds of fruit purchased Cost per pound
Bananas 3 $0.50
Tomatoes 2.5 $0.65
Apples 2 $0.75

A. Yes, Kim will spend $1.50 purchasing fruit.
Incorrect. $1.50 is not the constant product of all 3 pairs of numbers in the table.

B. No, there isn’t a constant of variation.
Correct!

C. Yes, Kim will spend $2 purchasing fruit.
Incorrect. For an inverse variation, the product of each pair of corresponding numbers is constant.

D. Yes, Kim will spend $6 purchasing fruit.
Incorrect. For an inverse variation, the product of each pair of corresponding numbers is constant.