Question

If y varies inversely with x and y = 9 when x = 2.5. How do you find y when x = - 0.6?

Answer 1

Hint: Now we are given that the two values are inversely proportional. Let the constant of proportionality be k. then we get $x=k\times \dfrac{1}{y}$ where k is the constant. Now using the first condition we will find the value of k. Now we will use this value of k in the second condition to find the required value of y.

Complete step by step solution:
Now we are given that y varies inversely with x. Hence we can say $y\prec \dfrac{1}{x}$ . Let k be the constant of proportionality. Hence we can say that $y=k\times \dfrac{1}{x}$ .
Now multiplying the whole equation with x we get, $y\times x=k$ .
Now this means that the value of $y\times x$ is constant for all values of x and y possible.
Now we are given that when x = 2.5 then the value of y = 9.
Hence we have $x\times y=2.5\times 9=22.5$ .
Hence we get the value of k which is constant is 22.5.
Hence now we have the equation as $x\times y=22.5$
Now we want to find the value of y when x = - 0.6.
Substituting the value of x in the equation $x\times y=22.5$ we get, $\left( -0.6 \right)\times y=22.5$
Now dividing the whole equation by $-0.6$ we get,
$\begin{align}
  & \Rightarrow y=\dfrac{22.5}{-0.6} \\
 & \Rightarrow y=-\dfrac{225}{6} \\
 & \Rightarrow y=-37.5 \\
\end{align}$

Hence when the value of x is – 0.6 then the value of y = - 37.5.

Note: Now note that when we have two quantities inversely proportional then their multiplication is constant. If the two values are directly proportional then the ratio of the two quantities will be constant.