Answer:
Yes, "y" varies directly with "x".
The equation is: [tex]y=1.375x[/tex]
Step-by-step explanation:
By definition, Direct variation equations have the following form:
[tex]y=kx[/tex]
Where "k" is the Constant of variation.
If you solve for "k", the equation is:
[tex]k=\frac{y}{x}[/tex]
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 [tex]y=11[/tex] by [tex]x=8[/tex] you get:
[tex]\frac{11}{8}=1.375[/tex]
- Divide [tex]y=22[/tex] by [tex]x=16[/tex]:
[tex]\frac{22}{16}=1.375[/tex]
- Dividing [tex]y=33[/tex] by [tex]x=24[/tex]:
[tex]\frac{33}{24}=1.375[/tex]
Since the quotient is constant, then "y" varies directly with "x" and the the Constant of variation is:
[tex]k=1.375[/tex]
Therefore, the equation for the Direct variation is:
[tex]y=1.375x[/tex]
