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Does the table show a direct proportional relationship? If so, what is the constant of proportionality?

Does the table show a direct proportional relationship? If so, what is the constant-example-1
User Isaac
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1 Answer

6 votes

Answer:

C. Yes, 3.5.

Explanation:

If there is a relationship of direct proportionality for every ordered pair of the table, then the constant of proportionality must the same for every ordered pair. The constant of proportionality (
k) is described by the following expression:


k = (y)/(x) (1)

Where:


x - Input.


y - Output.

If we know that
(x_(1), y_(1)) = (13, 45.5),
(x_(2), y_(2)) = (14, 49) and
(x_(3), y_(3)) = (15, 52.5), then the constants of proportionalities of each ordered pair are, respectively:


k_(1) = (y_(1))/(x_(1))


k_(1) = (45.5)/(13)


k_(1) = (7)/(2)


k_(2) = (y_2)/(x_2)


k_(2) = (49)/(14)


k_(2) = (7)/(2)


k_(3) = (y_(3))/(x_(3))


k_(3) = (52.5)/(15)


k_(3) = (7)/(2)

Since
k_(1) = k_(2) = k_(3), the constant of proportionality is 3.5.

User Damien Carol
by
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