Which equation has a constant of proportionality equal to $3$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $y=\frac{8}{5} x$ $\newline$ (B) $y=\frac{1}{3} x$ $\newline$ (C) $y=\frac{1}{4} x$ $\newline$ (D) $y=\frac{18}{6} x$

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Algebra 1

Identify equivalent linear expressions

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Q. Which equation has a constant of proportionality equal to

3

\newline

Choose

1

answer:

\newline

(A)

y=\frac{8}{5} x

\newline

(B)

y=\frac{1}{3} x

\newline

(C)

y=\frac{1}{4} x

\newline

(D)

y=\frac{18}{6} x

Understand concept of constant: Understand the concept of constant of proportionality. The constant of proportionality in an equation of the form $y = kx$ is the value of $k$ , where $k$ is a constant.
Identify constant of proportionality: Identify the constant of proportionality in each given equation. $\newline$ For equation (A) $y = \frac{8}{5}x$ , the constant of proportionality is $\frac{8}{5}$ . $\newline$ For equation (B) $y = \frac{1}{3}x$ , the constant of proportionality is $\frac{1}{3}$ . $\newline$ For equation (C) $y = \frac{1}{4}x$ , the constant of proportionality is $\frac{1}{4}$ . $\newline$ For equation (D) $y = \frac{18}{6}x$ , the constant of proportionality is $\frac{18}{6}$ .
Simplify constants if necessary: Simplify the constants of proportionality if necessary. $\newline$ For equation $D$ , simplify $\frac{18}{6}$ to get the constant of proportionality. $\newline$ $\frac{18}{6} = 3$
Compare to desired value: Compare the constants of proportionality to the desired value of $3$ . Equation (A) has a constant of proportionality of $\frac{8}{5}$ , which is not equal to $3$ . Equation (B) has a constant of proportionality of $\frac{1}{3}$ , which is not equal to $3$ . Equation (C) has a constant of proportionality of $\frac{1}{4}$ , which is not equal to $3$ . Equation (D) has a constant of proportionality of $3$ , which is equal to $3$ .
Choose equation with constant: Choose the equation with the constant of proportionality equal to $3$ . The equation with the constant of proportionality equal to $3$ is (D) $y = \frac{18}{6}x$ .