Question

It is given that √x and y are in direct proportion. If the difference in the values of y when x = 25 and when x = 4 is 42, find:

(a) an equation connecting x and y,
a) y = 2√x
b) y = 3√x
c) y = 4√x
d) y = 5√x

Answer 1

To find the equation connecting x and y, determine the constant of proportionality by comparing the values of y when x = 25 and x = 4. The constant of proportionality is 2. The equation connecting x and y is y = 2√x.

Step-by-step explanation:

To find the equation connecting x and y, we first need to determine the constant of proportionality. We are given that √x and y are in direct proportion. This means that when x increases by a certain factor, y will also increase by the same factor.

Let's find the constant of proportionality by comparing the values of y when x = 25 and x = 4. The difference in the values is 42.

So, y increases by 42 when x increases by 21 (25-4). Therefore, the constant of proportionality is 42/21 = 2.

The equation connecting x and y is y = 2√x. Therefore, the correct answer is (a) y = 2√x.