A fixed fee plus a per-unit charge is a linear model: the fixed fee is the cost at zero units, and the per-unit charge is added for each unit. To match a table, check the zero-input row, then evaluate the rule at the other inputs in Desmos. Don't confuse the rate with the starting fee, and check every row.
Hints
- Hint 1
The starting value is the cost when the input is . At zero miles, the per-mile charge disappears, but the fixed fee remains. What should the table show in its first row?
- Hint 2
A table row pairs an input with its output. Define the cost rule in Desmos, then evaluate it at one mile and four miles. Do both costs match the rows of the same table?
Step-by-step
Check the starting fee, then evaluate the costs
Step 1Find the zero-mile cost
The is the fixed starting fee, paid even when no miles are traveled. So at , the per-mile charge is and . Only the per-mile charge disappears at zero miles.
- Step 2
Find the one-mile cost
Type in Desmos, then type . Desmos prints , so a one-mile ride costs $5.50. The charge is added to the starting fee, not used in place of it.
- Step 3
Check the last row and match the table
Keep those lines and type . Desmos prints , so the three pairs are , , and . Match all three rows: the table with those pairs shows the taxi costs. Choice C.