To determine the correct linear function that models the total cost \(y\) for a single order of \(x\) cartridges at Elvin's store, we need to follow these steps:
1. Understand the Variables and Constants:
- \(x\) represents the number of cartridges ordered.
- \(y\) represents the total cost of the order.
- The flat shipping fee is fixed at \$5.25, regardless of the number of cartridges ordered.
- Each cartridge costs \$15.99.
2. Formulate the Total Cost Formula:
- Each cartridge adds \$15.99 to the total cost. If \(x\) cartridges are ordered, the cost for just the cartridges will be \(15.99 \times x\).
- In addition to the cost of the cartridges, the total cost \(y\) must also include the fixed shipping fee of \$5.25.
3. Construct the Linear Function:
- The total cost \(y\) can be modeled by adding the cost of the cartridges to the flat shipping fee.
- Thus, the function can be written as:
[tex]\[
y = 15.99x + 5.25
\][/tex]
4. Match the Formulated Function to the Given Options:
- Option A: \(y = 21.24x\): This option does not account for the separate cost per cartridge and the flat shipping fee.
- Option B: \(y = 15.99x + 5.25\): This matches the function we formulated.
- Option C: \(x = 21.24y\): This cannot be correct as it incorrectly places \(y\) as a variable when it should be the dependent variable.
- Option D: \(x = 15.99y + 5.25\): This wrongly ties the shipping cost to \(y\) and misplaces the roles of \(x\) and \(y\).
Therefore, the correct linear function that models the total cost, \(y\), for a single order of \(x\) cartridges is:
[tex]\[
\boxed{y = 15.99x + 5.25}
\][/tex]
The corresponding option is [tex]\(B\)[/tex].
