Chapter 5.2, Problem 19P

For the data in each table, tell whether $y$ varies directly with $x$.

If it does, write an equation for the direct variation.

To determine

To find: The table of values represent a direct variation or not if it does, find the equation.

Answer to Problem 19P

y is not directly varies with x .

Explanation of Solution

Given information: The table of values are

x	y
9	10.8
12	14.4
-3	3.6

Formula used: When y varies directly to x the equation is $y=kx$ . Where ‘ k’ is constant of direct variation. Formula to find constant of variation $k=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Let’s find constant of variation by taking two points from the table if constant of variation for all pair of points are same then it is direct variation.

For (9,10.8) and (12,14.4)

  $k=\frac{14.4-10.8}{12-9}$

  $=1.2$

For (12,14.4) and (-3,3.6)

  $k=\frac{3.6-14.4}{-3-12}$

  $=0.72$

Here constant of variation are not same for two different pair of points. So, it is y is not directly varies to x .