The table shows the price for different numbers of board games: Number of Board Games Price (in dollars)
2 7
4 14
5 17.50
9 31.50

Does this table of numbers represent a proportional relationship? (5 points)

a
Yes, because 3.5 times the price is the number of board games

b
Yes, because the price is 3.5 times the number of board games

c
No, because the price of 4 board games should be $9 and not $14

d
No, because the price of 9 board games should be $40.50 and not $31.50

We conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

Step-by-step explanation:

We know that when y varies directly with x, the equation is

y ∝ x

y = kx

k = y/x

where 'k' is called the proportionality constant.

From the table,

For the point (2, 7)

k = y/x

  = 7/2

  = 3.5

For the point (4, 14)

k = y/x

   = 14 / 4

   = 7/2

    = 3.5

For the point (5, 17.50)

k  = y/x

   = 17.5 / 5

   = 3.5

For the point (9, 31.50)

k  = y/x

   = 31.50 / 9

   = 3.5

From the above calculations, we computed that the value of the proportionality constant remains the same.

Thus, the table of numbers represents a proportional relationship.

Therefore, the equation becomes

y = kx

The price of 2 board game

y = 3.5 (2)

  = 7

The price of 4 board game

y = 3.5 (4)

  = 14

Therefore, we conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

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step-by-step explanation:

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