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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 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 initial values of Linear Function 1 and Linear Function 2, we need to identify their initial values.

Linear Function 1: Lionel’s cell phone plan costs $45 per month. This indicates that the cost starts at $45, so the initial value is $45.

Linear Function 2: The relationship is given by the equation \(y = 40x + 60\). The initial value (or y-intercept) occurs when \(x = 0\): \[ y = 40(0) + 60 = 60 \] Thus, the initial value for Linear Function 2 is $60.

Now, we can compare the two initial values:

  • Initial value of Linear Function 1 = $45
  • Initial value of Linear Function 2 = $60

Since $45 (Linear Function 1) is less than $60 (Linear Function 2), we conclude that:

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.