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

Answer 1

To compare the initial values of Linear Function 1 and Linear Function 2, let's look at each of them:

1. **Linear Function 1**: Lionel’s cell phone plan costs $45 per month. This means the cost starts at $45 when no months have passed, so the initial value is:
\[
\text{Initial Value (Function 1)} = 45
\]

2. **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 the equation:
\[
y = 40x + 60
\]
In this linear function, the initial value is the value of \(y\) when \(x = 0\):
\[
\text{Initial Value (Function 2)} = 40(0) + 60 = 60
\]

Now, comparing the initial values:
- Initial Value of Linear Function 1: **$45**
- Initial Value of Linear Function 2: **$60**

Thus, we find that **Linear Function 1 has the lesser initial value**.

The correct response is:
**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.**