To determine which equation has a constant of proportionality equal to 4, we can evaluate each equation by finding the ratio of the coefficients of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. Let's go through each option one by one.
### Option A: [tex]\(4y = 4x\)[/tex]
To find the constant of proportionality:
1. Divide both sides by [tex]\(4\)[/tex]:
[tex]\[
y = x
\][/tex]
So the constant of proportionality is:
[tex]\[
\frac{x}{y} = 1
\][/tex]
### Option B: [tex]\(4y = 12x\)[/tex]
To find the constant of proportionality:
1. Divide both sides by [tex]\(4\)[/tex]:
[tex]\[
y = 3x
\][/tex]
So the constant of proportionality is:
[tex]\[
\frac{x}{y} = 3
\][/tex]
### Option C: [tex]\(3y = 4x\)[/tex]
To find the constant of proportionality:
1. Divide both sides by [tex]\(3\)[/tex]:
[tex]\[
y = \frac{4}{3}x
\][/tex]
So the constant of proportionality is:
[tex]\[
\frac{x}{y} = \frac{4}{3} \approx 1.33
\][/tex]
### Option D: [tex]\(3y = 12x\)[/tex]
To find the constant of proportionality:
1. Divide both sides by [tex]\(3\)[/tex]:
[tex]\[
y = 4x
\][/tex]
So the constant of proportionality is:
[tex]\[
\frac{x}{y} = 4
\][/tex]
### Conclusion:
From the calculations, we see that the constant of proportionality equal to 4 corresponds to option D: [tex]\(3y = 12x\)[/tex]. Therefore, the equation with a constant of proportionality equal to 4 is:
D. [tex]\(3y = 12x\)[/tex]
