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

1 answer

To compare the two linear functions, we need to identify their initial values.

Linear Function 1: Lionel's cell phone plan costs $45 per month. In this case, the initial cost (at month 0) is $45.

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 equation, the initial value (when x = 0) can be determined: \[ y = 40(0) + 60 = 60 \] So the initial value for Linear Function 2 is $60.

Now, we can compare the initial values:

  • Linear Function 1: $45
  • Linear Function 2: $60

Since $45 (Linear Function 1) is less than $60 (Linear Function 2), 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.