Chapter 5, Problem 15CR

To determine

To write a direct variation equation that relates $x$ and $y$ and to find the value of $y$ when $x=7$ , given that $y=-4$ when $x=4$ .

Answer to Problem 15CR

Direct variation equation is $y=-x$ and $y=-7$ when $x=7$ .

Explanation of Solution

Given:

  $y=-4$ when $x=4$ .

Calculation:

Consider the direct variation equation as,

  $y=k\cdot x\to \left(1\right)$

Now put $y=-4$ and $x=4$ in equation (1), we get

  $\begin{array}{l}-4=k\cdot \left(4\right)\\ \Rightarrow k=-1\end{array}$

Therefore equation (1) becomes,

  $y=-x$

Now when $x=7$ ,

  $y=-7$