Answer:
The relationship B is different than the other three, because it has a different proportionality constant.
Step-by-step explanation:
All available options show direct relationships, which are defined as follows:
[tex]y\propto x[/tex]
[tex]y=k\cdot x[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]k[/tex] - Proportionality constant, dimensionless.
We proceed to use the following strategy based on the proportionality constant, that is:
[tex]k = \frac{y}{x}[/tex]
A different relationship must indicate a different proportionality constant:
Option A ([tex]x = 0.8[/tex], [tex]y = 4[/tex])
[tex]k = \frac{4}{0.8}[/tex]
[tex]k = 5[/tex]
Option B ([tex]x = 10[/tex], [tex]y = 55[/tex])
[tex]k = \frac{55}{10}[/tex]
[tex]k = 5.5[/tex]
Option C ([tex]x = 4[/tex], [tex]y = 20[/tex])
[tex]k = \frac{20}{4}[/tex]
[tex]k = 5[/tex]
Option D ([tex]x = 10[/tex], [tex]y = 50[/tex])
[tex]k = \frac{50}{10}[/tex]
[tex]k = 5[/tex]
The relationship B is different than the other three, because it has a different proportionality constant.
