Question

Each equation represents a proportional relationship. Choose the equations for which the constant of proportionality is 1/4

.
A) y = 4x
B) y = 0.25x
C) 4y = x
D) 32y = 8x
E) 1/4y = 2x

Answer 1

Answer: E)1/4y=2x

Explanation:

The constant of proportionality represents the ratio between the dependent and independent variables in a proportional relationship. If the constant of proportionality is 1/4, it means that the dependent variable is one-fourth the value of the independent variable.

So, we need to determine which equations have a constant of proportionality of 1/4:

A) y = 4x

The constant of proportionality in this equation is 4, not 1/4.

B) y = 0.25x

The constant of proportionality in this equation is 1/4.

C) 4y = x

The constant of proportionality in this equation is 1/4, since we can rewrite it as y = 1/4x.

D) 32y = 8x

We can simplify this equation by dividing both sides by 8:

4y = x

The constant of proportionality in this equation is 1/4.

E) 1/4y = 2x

We can rewrite this equation as:

y = 8x

The constant of proportionality in this equation is 8, not 1/4.

Therefore, the equations for which the constant of proportionality is 1/4 are B), C), and D).

Answer 2

B, C, D

Explanation:

You want to identify the equations that have a constant of proportionality of 1/4.

Proportional relation

A proportional relationship can be written in the form ...

y = kx

where k is the constant of proportionality.

You want to identify those relations that are equivalent to this with k=1/4.

Choices

A) y = 4x . . . . . k = 4 ≠ 1/4

B) y = 0.25x . . . . . k = 0.25 = 1/4

C) 4y = x ⇒ y = 1/4x . . . . . k = 1/4

D) 32y = 8x ⇒ y = 8/32x = 1/4x . . . . . k = 1/4

E) 1/4y = 2x ⇒ y = 2/(1/4)x = 8x . . . . . k ≠ 1/4

The relations with a constant of proportionality of 1/4 are B, C , D.

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