Questions: Which relationships have the same constant of proportionality between (y) and (x) as the following table? (x) (y) 2 7 (7 quad 24.5) (9 quad 31.5) Choose 3 answers: A (4 y=14 x) B (3.5 y=x)

Which relationships have the same constant of proportionality between (y) and (x) as the following table?
(x) (y)
2 7
(7 quad 24.5)
(9 quad 31.5)

Choose 3 answers:

A (4 y=14 x)
B (3.5 y=x)

Transcript text: Which relationships have the same constant of proportionality between $y$ and $x$ as the following table? \begin{tabular}{ll} $x$ & $y$ \\ \hline 2 & 7 \end{tabular} $7 \quad 24.5$ $9 \quad 31.5$ Choose 3 answers: A $4 y=14 x$ B $3.5 y=x$

Solution

Solution Steps

Step 1: Determine the constant of proportionality from the table

To find the constant of proportionality (k) between $ y $ and $ x $ in the table, use the formula $ y = kx $.

For $ x = 2 $ and $ y = 7 $: \[ k = \frac{y}{x} = \frac{7}{2} = 3.5 \]

Step 2: Verify the constant of proportionality for other pairs

Check if the same constant applies to the other pairs in the table.

For $ x = 7 $ and $ y = 24.5 $: \[ k = \frac{24.5}{7} = 3.5 \]

For $ x = 9 $ and $ y = 31.5 $: \[ k = \frac{31.5}{9} = 3.5 \]

The constant of proportionality is consistently 3.5.

Step 3: Check each given relationship for the same constant

Option A: $ 4y = 14x $

\[ y = \frac{14}{4}x = 3.5x \] This matches the constant of proportionality.

Option B: $ 3.5y = x $

\[ y = \frac{x}{3.5} \] This does not match the constant of proportionality.

Option C: Graph

The graph shows a line passing through (2, 7). The slope (constant of proportionality) is: \[ k = \frac{7}{2} = 3.5 \] This matches the constant of proportionality.

Option D: Graph

The graph shows a line passing through (1, 3.5). The slope (constant of proportionality) is: \[ k = \frac{3.5}{1} = 3.5 \] This matches the constant of proportionality.

Option E: Graph

The graph shows a line passing through (2, 10). The slope (constant of proportionality) is: \[ k = \frac{10}{2} = 5 \] This does not match the constant of proportionality.