he price of gas varies directly with the number of gallons purchased.

Question

Sim paid $48.77 for ​​​​​​​14.5 gallons of gas.

What is the constant of variation k?

(1 point)
Responses

k=0.30
k is equal to 0 point 3 0

k=34.27
k is equal to 34 point 2 7

k=3.36
k is equal to 3 point 3 6

k=63.27
k is equal to 63 point 2 7

Answer 1

To find the constant of variation \( k \), we can use the formula for direct variation:

\[ y = kx \]

Where:

• \( y \) is the total cost (in this case, $48.77),
• \( x \) is the number of gallons purchased (in this case, 14.5 gallons),
• \( k \) is the constant of variation.

We can rearrange the equation to solve for \( k \):

\[ k = \frac{y}{x} \]

Substituting the values:

\[ k = \frac{48.77}{14.5} \]

Now, performing the calculation:

\[ k \approx 3.36 \]

So, the constant of variation \( k \) is approximately 3.36.

The correct response is:

k=3.36.