Chapter 5.2, Problem 20P

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: Whether y varies directly with x for the table of values. If it does, write an equation for direct variation.

Answer to Problem 20P

Yes! y varies directly to x . The equation is $y=3x$ .

Explanation of Solution

Given information: The table of values are

x	y
-6.5	-19.5
-5.2	-15.6
4.8	14.4

Formula used: $y=kx$ , where ‘ k’ is constant of variation. Find k using formula $k=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

Let’s find the constant of variation using different pair of points from the table.

For (-6.5,-19.5) and (-5.2, -15.6)

  $k=\frac{-15.6+19.5}{-5.2+6.5}$

  $=3$

For (-5.2,-15.6) and (4.8,14.4)

  $k=\frac{14.4+15.6}{4.8+5.2}$

  $=3$

Hence, the value of kare constant. So y varies directly with x .

Constant of variation $k=3$

So, to write equation plug in k as 3 into the $y=kx$

The equation is

  $y=3x$

Conclusion: y varies directly with x . The equation is $y=3x$ .