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Which equation has a constant of proportionality equal to 1 ?
Choose 1 answer:
(A)
y=(10)/(11)x
(B)
y=(7)/(8)x
(c)
y=(3)/(15)x
(D)
y=x

Which equation has a constant of proportionality equal to $1$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $y=\frac{10}{11} x$ $\newline$ (B) $y=\frac{7}{8} x$ $\newline$ (C) $y=\frac{3}{15} x$ $\newline$ (D) $y=x$

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Identify linear and exponential functions

Full solution

Q. Which equation has a constant of proportionality equal to

1

?

\newline

Choose

1

answer:

\newline

(A)

y=\frac{10}{11} x

\newline

(B)

y=\frac{7}{8} x

\newline

(C)

y=\frac{3}{15} x

\newline

(D)

y=x

Identify Constant of Proportionality: The constant of proportionality in a linear equation $y = kx$ is the value of $k$ , where $k$ is a constant. We need to find the equation where $k$ equals $1$ .
Examine Option (A): Let's examine option (A) $y = \frac{10}{11}x$ . The constant of proportionality here is $\frac{10}{11}$ , which is not equal to $1$ .
Look at Option (B): Now, let's look at option (B) $y = \frac{7}{8}x$ . The constant of proportionality here is $\frac{7}{8}$ , which is also not equal to $1$ .
Consider Option (C): Next, we consider option (C) $y = \frac{3}{15}x$ . Simplifying $\frac{3}{15}$ gives us $\frac{1}{5}$ , so the constant of proportionality is $\frac{1}{5}$ , not $1$ .
Check Option (D): Finally, we check option (D) $y = x$ . Here, the constant of proportionality is $1$ because $y$ is directly equal to $x$ without any other factors. This means that for every unit increase in $x$ , $y$ increases by the same amount, which is the definition of a constant of proportionality of $1$ .

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