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






StartFraction 10 x Over 3 y EndFraction = 1

The graph has a greater constant of variation.
The equation has a greater constant of variation.
The constant of variation is the same for the graph and the equation.
The constant of variation cannot be compared because the equation is nonproportional.

Answer 1

The equation representing the direct variation between Jalen's mobile phone cost
`(\(y\))` and the number of minutes
`(\(x\)) is \(y = 0.05x\).` The constant of variation is 0.05, showing a proportional relationship.

The relationship between the cost
`\(y\)` and the number of minutes
`\(x\)` is said to vary directly if it can be expressed in the form
`\(y = kx\),` where
`\(k\)` is the constant of proportionality or constant of variation.

Given the information in the table, let's find the constant of variation
`(\(k\))`:

1. For the first data point (150 minutes, $7.50):
`\(k = (7.50)/(150) = 0.05\)`

2. For the second data point (220 minutes, $11.00):
`\(k = (11.00)/(220) = 0.05\)`

3. For the third data point (250 minutes, $12.50):
`\(k = (12.50)/(250) = 0.05\)`

4. For the fourth data point (275 minutes, $13.75):
`\(k = (13.75)/(275) = 0.05\)`

Since
`\(k\)` is consistently 0.05 for all data points, the equation representing the variation is
`\(y = 0.05x\).`

Therefore, among the given options, the correct equation representing the variation is:

`\[ y = 0.05x \]`

Now, let's address the statement:

`\[ (10x)/(3y) = 1 \]`

By rearranging this equation, we get:

`\[ (10)/(3) = (x)/(y) \]`

This implies that the constant of variation
`(\(k\))` is
`\((10)/(3)\)` , which is not the same as the constant of variation found earlier
`(\(k = 0.05\))`. Therefore, the statement "The constant of variation is the same for the graph and the equation" is false.

So, the correct statement is: The constant of variation cannot be compared because the equation is nonproportional.