Question

The table shows the number of minutes Jalen talks on his mobile phone and the cost of the phone calls.

Jalen’s Mobile Phone Cost
Number of minutes, x
150
220
250
275
Cost, y
$7.50
$11.00
$12.50
$13.75

If the cost varies directly with the number of minutes Jalen talks on the phone, which equation represents the variation?
y = 0.05 x
y = 20 x
y = 157.5 x
y = 1125 x

Answer 1

To find the equation that represents the direct variation between the cost \( y \) and the number of minutes \( x \) that Jalen talks on the phone, we can use the relationship that if \( y \) varies directly with \( x \), then \( y = kx \), where \( k \) is the constant of variation.

We can determine \( k \) using one of the given pairs of minutes and cost. Let's use the first pair:

- For \( x = 150 \) minutes, \( y = 7.50 \).

Using the formula \( y = kx \):

\[
7.50 = k \cdot 150
\]

Solving for \( k \):

\[
k = \frac{7.50}{150} = 0.05
\]

Now that we have \( k \), we can write the equation:

\[
y = 0.05x
\]

Thus, the equation that represents the variation is:

\[
y = 0.05x
\]

Therefore, **the correct answer is \( y = 0.05x \)**.