Question

Which equation has a constant of proportionality equal to
\[10\]?
Choose 1 answer:
Choose 1 answer:
(Choice A)

\[y=\dfrac{2}{20}x\]
A

\[y=\dfrac{2}{20}x\]
(Choice B, Checked)

\[y=\dfrac{30}{3}x\]
B

\[y=\dfrac{30}{3}x\]
(Choice C)

\[y=\dfrac{12}{2}x\]
C

\[y=\dfrac{12}{2}x\]
(Choice D)

\[y=\dfrac{5}{5}x\]
D

\[y=\dfrac{5}{5}x\]

Answer 1

To identify which equation has a constant of proportionality equal to \( 10 \), we need to analyze each option. The constant of proportionality \( k \) in a direct variation equation of the form \( y = kx \) is simply the coefficient of \( x \).

Let's simplify the coefficients for each choice:

- **Choice A:**
\[ y = \frac{2}{20}x = \frac{1}{10}x \quad (k = \frac{1}{10}) \]

- **Choice B:**
\[ y = \frac{30}{3}x = 10x \quad (k = 10) \]

- **Choice C:**
\[ y = \frac{12}{2}x = 6x \quad (k = 6) \]

- **Choice D:**
\[ y = \frac{5}{5}x = 1x \quad (k = 1) \]

Among all the choices, **Choice B** \( y = \frac{30}{3}x \) simplifies to \( y = 10x \), which has a constant of proportionality equal to \( 10 \).

Thus, the answer is **Choice B**.