Question

Suppose Y varies directly as X, and y = 9 when x = 3/2. Find y when x = 1.

Answer 1

to vary directly is to be in proportion

y/x = y/x

9/(3/2) = y
9(2/3) = y
y = 6

Answer 2

Answer:  The required value of y is 6.

Step-by-step explanation: We are given that y varies directly as x and y = 9 when $x=\dfrac{3}{2}.$

We are to find the value of y when x = 1.

According to the given information, we have

$y\propto x\\\\\Rightarrow y=k\times x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{where k is the constant of integration}]\\\\\Rightarrow y=kx~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

When y = 9 and $x=\dfrac{3}{2},$ we have from equation (i) that

$9=k\times\dfrac{3}{2}\\\\\\\Rightarrow k=\dfrac{18}{3}\\\\\Rightarrow k=6.$

So, equation (i) becomes

$y=6x.$

Therefore, when x = 1, we get

$y=6\times1=6.$

Thus, the required value of y is 6.