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Decide whether each table could represent a proportional relationship. If the
relationship could be proportional, what would be the constant of proportionality?

Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would be the constant of proportionality? class=

Answer :

Answer:

Step-by-step explanation:

If given tables in the picture show the proportional relationship,

Number of wheels (w) ∝ Number of buses (b)

w ∝ b

w = kb

Here, k = proportionality constant

k = [tex]\frac{w}{b}[/tex]

Number of buses (b)           Number wheels (w)             Wheels per bus [tex](\frac{w}{b})[/tex]

          5                                           30                               [tex]\frac{30}{5}=6[/tex]              

          8                                           48                               [tex]\frac{48}{8}=6[/tex]

         10                                           60                               [tex]\frac{60}{10}=6[/tex]

         15                                           90                               [tex]\frac{90}{15}=6[/tex]

Here, proportionality constant is 6.

Similarly, If number of wheels (w) ∝ Number of train cars (t)

w = kt

Here, k = proportionality constant

k = [tex]\frac{w}{t}[/tex]

Number of train cars(t)          Number of wheels(w)     Wheels per train car ([tex]\frac{w}{t}[/tex])

              20                                        184                           [tex]\frac{184}{20}=9.2[/tex]

              30                                        264                           [tex]\frac{264}{30}=8.8[/tex]

              40                                        344                           [tex]\frac{344}{40}=8.6[/tex]

              50                                        424                           [tex]\frac{424}{50}=8.48[/tex]

Since, ratio of w and t is not constant, relation between number of wheels and number of train cars is not proportional.

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