Question

In a-c, the value of y varies directly with x. Find k, the constant of proportionality.

a. x=-2, y=20
b. x=7, y=3
c. x=81, y=9

a) k=

Answer 1

The constant of proportionality (k) when y varies directly with x should be the same for all values of x and y. k=y/x.

Step-by-step explanation:

When two variables are directly proportional, the ratio of their values remains constant. This constant ratio is referred to as the constant of proportionality, often denoted by the symbol k. To find the value of k when given pairs of x and y values where y varies directly with x, we can use the formula y = kx. By rearranging this formula, we can solve for k by dividing y by x: k = y / x.

Given the pairs of values from the question:

• When x = -2 and y = 20: k = 20 / (-2) = -10.
• When x = 7 and y = 3: k = 3 / 7. As this does not match the previous value of k, we must investigate further.
• When x = 81 and y = 9: k = 9 / 81 = 1 / 9. This is also inconsistent with the first pair's k value.

The question might contain a mistake since k should be the same for all pairs of x and y if y is directly proportional to x. For any correct pair, the correct option for the constant of proportionality k will be the ratio of y to x for that pair. However, since the values provided do not result in a consistent k, further clarification is needed from the student.