Question

1) For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.​

Answer 1

Answer:

Yes, "y" varies directly with "x".

The equation is:  $y=1.375x$

Step-by-step explanation:

 By definition, Direct variation equations have the following form:

$y=kx$

Where "k" is the Constant of variation.

If you solve for "k", the equation is:

$k=\frac{y}{x}$

Then, given the table provided in the exercise, you can know if "y" varies directly with "x" by finding the quotient of the correspoding values of "x" and "y":

- Dividing  $y=11$ by $x=8$ you get:

$\frac{11}{8}=1.375$

- Divide $y=22$ by $x=16$:

$\frac{22}{16}=1.375$

- Dividing  $y=33$ by $x=24$:

$\frac{33}{24}=1.375$

Since the quotient is constant, then "y" varies directly with "x" and the the Constant of variation is:

$k=1.375$

Therefore, the equation  for the Direct variation is:

$y=1.375x$