Chapter 5.2, Problem 17PPE

To determine

To calculate:the value of y when x=12.

Answer to Problem 17PPE

  $x=12$ , thenvalue of $y$ is $30$ .

Explanation of Solution

Given information:

  $y$ varies directly with $x$ .

The direct variation equation relates $x$ and $y$ .

System equation: $y=5,x=2$

Calculation: Finding the equation for direct variance relates to $x$ and $y$ as follows:

An equation is referred to as a direct variation when it in the form of $y=kx,$ where, $k\ne 0$ is the constant of variation.

The value of the variance constant is obtained by diving $x$

  $k=\frac{y}{x}$

Let the direct variation equation be $y=kx$

The function is $y=kx$

Substitute $2$ for $x$ and $5$ for $y$

  $\begin{array}{l}5=k(2)\\ 5=2k\end{array}$

Divide both sides by 2 to solve for $k$

  $5=2k÷2$

  $\frac{5}{2}=k$

Write an equation: $y=\frac{5}{2}x$

Substitute $\frac{5}{2}$ for $k$ in $y=kx$

The equation $y=\frac{5}{2}x$ relates $x$ and $y.$ when $y=5,x=2$

  $\begin{array}{l}\text{If }x=12\\ y=\frac{5}{2}x\\ =\frac{5}{2}\left(12\right)\\ =\frac{5}{1}\left(6\right)\\ =5\left(6\right)\\ =30\end{array}$

Therefore, the value of $y$ is $30$ ,when $x=12$