Chapter 5.2, Problem 16PPE

To determine

To determine variation equation that relates $x$ and $y.$

Answer to Problem 16PPE

  $y=\frac{5}{2}\times x$

Explanation of Solution

Given:

  $y=7\frac{1}{2}$ when $x=3$

  $x=12$

Calculation:

Let’s consider the equation as,

  $\Rightarrow y=kx$

Substituting the values of $x$ and $y$ ,

  $\Rightarrow 7\frac{1}{2}=k\times 3$

  $\Rightarrow \frac{15}{2}=k\times 3$

  $\Rightarrow k=\frac{5}{2}$

So,

  $\Rightarrow y=kx$

  $\Rightarrow y=\frac{5}{2}\times x\to (i)$

Now, when the value of $x=12$ ,

Value of $y$ is,

Putting the value $x$ in equation (i),

  $\Rightarrow y=\frac{5}{2}\times 12$

  $\Rightarrow y=30$

Conclusion:

Therefore, the variation equation that relates $x$ and $y$ is $y=\frac{5}{2}\times x.$