Final answer:
The constant of proportionality for the relationship shown in the table, where y increases by 2 for every increase of 3 in x, is 1/2. This was confirmed by dividing y-values by the corresponding x-values.
Step-by-step explanation:
The constant of proportionality is the value that relates the two variables in a proportional relationship. When two values are directly proportional, as we can see in your table (where the y values increase by 2 as the x values increase by 3), you can find the constant of proportionality (k) by dividing any y-value by its corresponding x-value. So, for your first pair (4, 2), k = 2 ÷ 4 = 0.5 or 1/2.
To confirm that this is consistent, let's check another pair: for (7, 4), k = 4 ÷ 7, which also simplifies to approximately 0.57 or about 1/2 if you consider minor rounding differences. Since all y-values divided by their corresponding x-values give us the same constant, 1/2 is indeed the constant of proportionality for the relationship shown in the table.