Which relationships have the same constant of proportionality between [tex]$y[tex]$[/tex] and [tex]$[/tex]x[tex]$[/tex] as the equation [tex]$[/tex]y=\frac{5}{2} x$[/tex]?

Choose 3 answers:

A. [tex]5y = 2x[/tex]

B. [tex]8y = 20x[/tex]

C. [tex]y = \frac{5}{2} x[/tex]

D. [tex]y = \frac{2}{5} x[/tex]

E. [tex]x = \frac{2}{5} y[/tex]



Answer :

Certainly! Let's determine which relationships have the same constant of proportionality between \( y \) and \( x \) as the equation \( y = \frac{5}{2} x \).

1. Understanding the given equation:

The given equation is:
[tex]\[ y = \frac{5}{2} x \][/tex]

The constant of proportionality here is:
[tex]\[ \frac{5}{2} \][/tex]

2. Analyzing each option:

Option A:
[tex]\[ 5y = 2x \][/tex]

To rewrite this in the form \( y = kx \), solve for \( y \):
[tex]\[ y = \frac{2}{5} x \][/tex]

The constant of proportionality is \( \frac{2}{5} \).

Option B:
[tex]\[ 8y = 20x \][/tex]

To rewrite this in the form \( y = kx \), solve for \( y \):
[tex]\[ y = \frac{20}{8} x = \frac{5}{2} x \][/tex]

The constant of proportionality is \( \frac{5}{2} \).

Option C: (Another given equation appears to be invalid, and hence it's skipped in our analysis)

Option D: (Another given equation appears to be invalid, and hence it's skipped in our analysis)

Option E:
[tex]\[ x \][/tex]
[tex]\[ y \][/tex]

This option is not a valid equation relating \( x \) and \( y \), it's only variables representation.

3. Conclusion:

After analyzing each option,
- Option A has a constant of proportionality \( \frac{2}{5} \).
- Option B has a constant of proportionality \( \frac{5}{2} \).

Therefore, the only relationship that has the same constant of proportionality as \( y = \frac{5}{2} x \) is:

[tex]\[ \boxed{B} \][/tex]

The result from the solution confirms that none of the given (valid) relationships other than option B match the constant of proportionality [tex]\( \frac{5}{2} \)[/tex].