Question

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

Answer 1

Answer:

C. Yes, 3.5.

Step-by-step 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:

$k = \frac{y}{x}$ (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:

$k_{1} = \frac{y_{1}}{x_{1}}$

$k_{1} = \frac{45.5}{13}$

$k_{1} = \frac{7}{2}$

$k_{2} = \frac{y_2}{x_2}$

$k_{2} = \frac{49}{14}$

$k_{2} = \frac{7}{2}$

$k_{3} = \frac{y_{3}}{x_{3}}$

$k_{3} = \frac{52.5}{15}$

$k_{3} = \frac{7}{2}$

Since $k_{1} = k_{2} = k_{3}$, the constant of proportionality is 3.5.