Chapter 5.2, Problem 15PPE

To determine

To calculate:value of y when x=12.

Answer to Problem 15PPE

  $x=12$ , then the value of $y$ is $-60$ .

Explanation of Solution

Given information:

System equation: $y=-10,x=2$

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

  $y$ varies directly with $x$

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 $-10$ for $y$

  $-10=k(2)$

  $-10=2k$

Divide both sides by 2 to solve for $k$

  $-10=2k÷2$

  $-5=k$

Write an equation: $y=-5x$

Substitute $-5$ for $k$ in $y=kx$

The equation $y=-5x$ relates $x$ and $y.$ when $y=-10,x=2$

  $\begin{array}{l}\text{If }x=12\\ y=-5x\\ =-5(12)\\ =-60\end{array}$

Therefore, the value of $y$ is $-60$ ,when $x=12$