Chapter 9.4, Problem 14HP

To determine

To determine find the mistake in given solution.

Answer to Problem 14HP

To determines the direct variation check slope of line will be positive or indirect variation check slope of line will be negative.

Explanation of Solution

Given:

Graph with points $(2,12)$ and $(6,18)$

  

Calculation:

Find the mistake in given solution.

Here slope of the line can be obtained as,

  $\begin{array}{l}\text{slope}\text{of}\text{line}=\frac{\text{change}\text{in}y}{\text{change}\text{in }x}\\ m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{18-12}{6-2}\\ m=\frac{6}{4}\\ m=1.5\end{array}$

Therefore,

A constant slope does not mean direct variation, but the sign of the slope determines the direct variation. So, the mistake in the solution, is variation does not depend on constant of variation but sign of the constant of variation.