Question

Steven has determined that there is a proportional relationship that exists between the amount of time he works out each day to the amount of time he is able to focus on homework later on. Identify the constant of proportionality that exists between time spent exercising and time spent focusing.

Answer 1

The constant of proportionality k in the directly proportional relationship between x and y, where y = 5 when x = 4, is found to be 1.25, and the equation is y = 1.25x.

Step-by-step explanation:

Given that there is a directly proportional relationship between two quantities, x and y, and knowing that when x = 4, y = 5, we can write the equation of direct proportionality as y = kx, where k is the constant of proportionality.

To find the value of k, we use the given values of x and y:

• y = kx
• 5 = k(4)

Then we solve for k:

• k = 5 / 4
• k = 1.25

Therefore, the constant of proportionality k is 1.25, and the equation representing this direct relationship is y = 1.25x.

Complete question:

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There exists a direct relationship between two quantities, x and y, such that when x = 4, y = 5. Write an equation and find k, the constant of proportionality for this relation.