Question

Compare Linear Function 1 with Linear Function 2. Which one has the lesser initial value?

Linear Function 1: Lionel’s cell phone plan costs $45 per month.
Linear Function 2: The relationship between the number of months Ruby has had her cell phone (x)
and the total cost (y)
is given by y=40x+60
.
(1 point)
Responses

Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $60.
Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $60.

Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $40.
Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $40.

Linear Function 2 has the lesser initial value, with an initial value equal to $40 while Linear Function 1 has an initial value equal to $45.
Linear Function 2 has the lesser initial value, with an initial value equal to $40 while Linear Function 1 has an initial value equal to $45.

Linear Function 1 has the lesser initial value, with an initial value equal to $45 while Linear Function 2 has an initial value equal to $60.

Answer 1

To compare the initial values of the two linear functions:

1. **Linear Function 1**: Lionel’s cell phone plan costs $45 per month.
- This suggests a constant cost of $45 per month, which can be represented as:
\[
y = 45x
\]
- The initial value (when x = 0, before any months have passed) is $0.

2. **Linear Function 2**: The total cost y is given by the equation \( y = 40x + 60 \).
- In this equation, the initial value (when x = 0) can be found by substituting 0 for x:
\[
y = 40(0) + 60 = 60
\]
- So, the initial value for Linear Function 2 is $60.

Now we compare the initial values:
- Linear Function 1 has an initial value of $0.
- Linear Function 2 has an initial value of $60.

**Conclusion**: Linear Function 1 has the lesser initial value ($0) compared to Linear Function 2 ($60).

The correct response is:
**Linear Function 1 has the lesser initial value, with an initial value equal to $0 while Linear Function 2 has an initial value equal to $60.**