Question

A table shows a proportional relationship where k is the constant of proportionality. the rows are then switched. how does the new constant of proportionality relate to the original one?"

Answer 1

Assuming that the proportional relationship that the table has and k is directly proportional, we can say that it may equal to the size of the existing switched row, speculating again that the size of the table is equilateral –equal in size. Then there’s no new change. Hence direct proportionality and indirect proportionality is what matters in the relationship since k will define the number of which will change the course of the equation, somehow k is like the independent variable in the given formula.

Answer 2

The correct answer is:

The new constant of proportionality is the reciprocal of the original one.

Explanation:

A proportional relationship is in the form y=kx, where k is the constant of proportionality.

If the rows are switched, this means that the values of x and y are switched. This gives us the equation

x = ky

To solve for y, we will divide both sides by k:

x/k = (ky)/k

x/k = y

x/k is the same as x(1/k); this makes the new constant of proportionality 1/k, which is the reciprocal of k.