Let's go through each of the problems step by step to provide solutions.

Problem 1:

The table shows a proportional relationship between the number of cups of water (x) and pancake mix (y).

• a) Enter the number of cups of pancake mix used for 1 cup of pancake mix.
  From the table, for every 1 cup of water, there are 2 cups of pancake mix.

• b) Enter the constant of proportionality that relates the quantities $x$ and $y$.
  The constant of proportionality (k) is the ratio $\frac{y}{x}$. From the table,
  $k = \frac{2}{1} = 2$.

• c) Enter an equation that relates the quantities.
  Since $y = kx$, the equation is $y = 2x$.

Problem 2:

The table shows a proportional relationship between the number of cups of chocolate powder (x) and milk (y).

• a) Enter the number of cups of chocolate powder used for 1 cup of milk.
  To find this, we need to use the ratio from the table. From row 1:
  $\frac{4}{5}$, so 0.8 cups of chocolate powder is used for 1 cup of milk.

• b) Enter the constant of proportionality that relates the quantities $x$ and $y$.
  Using the ratio $k = \frac{y}{x} = \frac{5}{4} = 1.25$, the constant of proportionality is 1.25.

• c) Enter an equation that relates the quantities.
  The equation is $y = 1.25x$.

Problem 3:

The table shows a proportional relationship between the number of cups of peach juice (x) and lemonade (y).

• a) Enter the number of cups of peach juice used for 1 cup of lemonade.
  Using the ratio from the first row: $\frac{4}{6} = 0.67$. So, 0.67 cups of peach juice are used for 1 cup of lemonade.

• b) Enter the constant