What you’ll learn
Represent relationships using equations.
Key idea
Keep the fixed charge separate from the variable charge; the output depends on the chosen distance.
A fixed charge is included once; remove it before dividing when working backward to the input.
Worked example
Enter the exact value or ordered values in the format requested below.
A ride costs C=2+2m dollars for m miles. Enter the numeric cost when m=6.
- C=2+2m includes a fixed charge and a per-mile charge.
- At m=6, C=2+12=14; recover m by removing 2 then dividing by 2.
Answer: 14
Quick Check
Evaluate a worked attempt at represent relationships using equations, identify the first invalid step, and provide the correction.
Using C=4+2m at m=9, a student writes Step 1: C=4+2(9). Step 2: C=18, discarding the fixed charge. Locate the first invalid step and correct the cost.