Question

y varies inversely with x. if y=7 when x= -4, find y when x=2

Answer 1

SOLUTION:

Step 1:

In this question, we are given the following:

y varies inversely with x. if y=7 when x= -4, find y when x=2

Step 2:

Mathematically, we have that:

$\begin{gathered} y\text{ }\propto\text{ }\frac{1}{x} \\ y\text{ =}\frac{k}{x},\text{ where k is a constant} \end{gathered}$$\begin{gathered} \text{when x= -4, then y = 7} \\ 7\text{ = }\frac{k}{-4} \\ \end{gathered}$

cross-multiply, we have that:

$\begin{gathered} k\text{ = 7 x - 4} \\ k\text{ = -28} \end{gathered}$

Hence, the relationship between x and y is:

$y\text{ =}\frac{-28}{x}$

Step 3:

Since,

$\begin{gathered} y\text{ = }\frac{-28}{x} \\ \text{when x = 2, we have that:} \\ y\text{ = }\frac{-28}{2} \\ y\text{ = -14} \end{gathered}$

CONCLUSION:

When x = 2 , then y = -14