To determine which equation has a constant of proportionality equal to 2, let's examine each option:
1. Equation (A):
[tex]\[
y = \frac{10}{5} x
\][/tex]
Simplify the fraction:
[tex]\[
\frac{10}{5} = 2
\][/tex]
Thus, equation (A) becomes:
[tex]\[
y = 2x
\][/tex]
Here, the constant of proportionality is 2.
2. Equation (B):
[tex]\[
y = \frac{2}{2} x
\][/tex]
Simplify the fraction:
[tex]\[
\frac{2}{2} = 1
\][/tex]
Thus, equation (B) becomes:
[tex]\[
y = 1x = x
\][/tex]
Here, the constant of proportionality is 1.
3. Equation (C):
[tex]\[
y = \frac{2}{4} x
\][/tex]
Simplify the fraction:
[tex]\[
\frac{2}{4} = \frac{1}{2}
\][/tex]
Thus, equation (C) becomes:
[tex]\[
y = \frac{1}{2}x
\][/tex]
Here, the constant of proportionality is [tex]\( \frac{1}{2} \)[/tex].
4. Equation (D):
[tex]\[
y = \frac{22}{2} x
\][/tex]
Simplify the fraction:
[tex]\[
\frac{22}{2} = 11
\][/tex]
Thus, equation (D) becomes:
[tex]\[
y = 11x
\][/tex]
Here, the constant of proportionality is 11.
From the above analysis, we can clearly see that only equation (A):
[tex]\[
y = \frac{10}{5} x \implies y = 2x
\][/tex]
has a constant of proportionality equal to 2.
Therefore, the correct answer is:
(A) [tex]\( y = \frac{10}{5} x \)[/tex]
