Question

Two quantities, x and y, are directly proportional. If x is tripled, what happens to y? (20 points)

a) It is multiplied by 1/3
b) It is tripled
c) It is multiplied by 9
d) It depends on the starting value of x

Answer 1

b) It is tripled

Explanation:

If x is directly proportional to y, then

x = ky ... 1

Wherw y = x/k

where k is the constant of proportionality.

If x is tripled, the equation becomes

3x = kyo ... 2

From equation 2, yo = 3x/k

Where yo is the new value of y when x is tripled

Based in the new value of y, it can be seen that y also tripled as x tripled.

Note that in a direct variation, increase or decrease in a variable leads to equal increase or decrease in the other variable.

Answer 2

If x and y are directly proportional, that means Y = kX. The variable k here is a constant. When we say x is tripled, k must be 3.

Let's have an example. Let's assume that x is 5. If we triple 5, it would equal to 15.

y = 3(5)
15 = 15

Therefore, the answer to this problem would be:
b) It is tripled