Question

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

Answer 1

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{ }(1)/(x) \\ y\text{ =}(k)/(x),\text{ where k is a constant} \end{gathered}`
`\begin{gathered} \text{when x= -4, then y = 7} \\ 7\text{ = }(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{ =}(-28)/(x)`

Step 3:

Since,

`\begin{gathered} y\text{ = }(-28)/(x) \\ \text{when x = 2, we have that:} \\ y\text{ = }(-28)/(2) \\ y\text{ = -14} \end{gathered}`

CONCLUSION:

When x = 2 , then y = -14