Which equation has a constant of proportionality equal to $9$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $y=\frac{81}{3} x$ $\newline$ (B) $y=9 x$ $\newline$ (C) $y=3 x$ $\newline$ (D) $y=\frac{1}{9} x$

Full solution

Q. Which equation has a constant of proportionality equal to

9

\newline

Choose

1

answer:

\newline

(A)

y=\frac{81}{3} x

\newline

(B)

y=9 x

\newline

(C)

y=3 x

\newline

(D)

y=\frac{1}{9} x

Understand concept of constant: Understand the concept of constant of proportionality. The constant of proportionality in a direct variation $y = kx$ is the value of $k$ where $y$ varies directly with $x$ .
Analyze option (A): Analyze option (A) $y = \frac{81}{3}x$ . Simplify the equation to find the constant of proportionality. $y = \frac{81}{3}x$ simplifies to $y = 27x$ . The constant of proportionality here is $27$ .
Analyze option (B): Analyze option (B) $y = 9x$ . The equation is already in the form $y = kx$ , where $k$ is the constant of proportionality. Here, the constant of proportionality is $9$ .
Analyze option (C): Analyze option (C) $y = 3x$ . The equation is in the form $y = kx$ , where $k$ is the constant of proportionality. Here, the constant of proportionality is $3$ .
Analyze option (D): Analyze option (D) $y = \frac{1}{9}x$ . The equation is in the form $y = kx$ , where $k$ is the constant of proportionality. Here, the constant of proportionality is $\frac{1}{9}$ .
Compare constants with required: Compare the constants of proportionality found in steps $2-5$ with the required constant of proportionality, which is $9$ . $\newline$ Option (A) has a constant of $27$ , option (B) has a constant of $9$ , option (C) has a constant of $3$ , and option (D) has a constant of $\frac{1}{9}$ . $\newline$ Only option (B) has the constant of proportionality equal to $9$ .