Let's carefully analyze the problem to determine the correct equation that represents the given scenario.
1. Initial Connection Fee:
- We have a fixed initial connection fee of \[tex]$1.35.
2. Cost Per Minute:
- The cost for each minute of talking on the phone is ten cents, which can be expressed as \$[/tex]0.10 per minute.
We need to create an equation that includes both the fixed connection fee and the variable cost based on the number of minutes talked.
Let's define the variables:
- [tex]\( x \)[/tex] represents the number of minutes talked.
- [tex]\( y \)[/tex] represents the total cost of the call.
The total cost of the call ([tex]\( y \)[/tex]) is composed of two parts:
1. The initial connection fee of \[tex]$1.35.
2. The variable cost which depends on the number of minutes (\( x \)) at a rate of \$[/tex]0.10 per minute.
Combining these, the equation will be:
[tex]\[ y = 0.10 \cdot x + 1.35 \][/tex]
Now we will verify each provided option to see which correctly represents this relationship:
- Option a: [tex]\( y = 1.35 x + 0.10 \)[/tex]
- This suggests \[tex]$1.35 per minute plus an additional ten cents, which is incorrect.
- Option b: \( y = 0.10 x + 1.35 \)
- This correctly accounts for the initial connection fee of \$[/tex]1.35 and the rate of \[tex]$0.10 per minute.
- Option c: \( y = 1.35 x + 10 \)
- This suggests \$[/tex]1.35 per minute plus a fixed cost of \[tex]$10, which is incorrect.
- Option d: \( y = 10 x + 1.35 \)
- This suggests \$[/tex]10 per minute plus the initial fee of \$1.35, which is incorrect.
Based on our analysis, the correct equation that best represents the scenario is:
[tex]\[ \boxed{b. \, y = 0.10 x + 1.35} \][/tex]
