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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.

1 answer

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.