Ask a New Question
Menu

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 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 $0 while Linear Function 2 has an initial value equal to $40.

1 answer

To compare the initial values of Linear Function 1 and Linear Function 2, we can analyze each function.

Linear Function 1:

  • Lionel’s cell phone plan costs $45 per month. This means that the total cost starts at $45 when \(x = 1\). However, if we consider \(x = 0\) (when he hasn't had the plan for any months), the cost is essentially $0. For each additional month, the cost increases by $45, but the initial value when \(x=0\) is $0.

Linear Function 2:

  • The equation is given by \(y = 40x + 60\). Here, the initial value occurs when \(x = 0\). Substituting \(x = 0\) into the equation gives: \[ y = 40(0) + 60 = 60 \] Therefore, the initial value of Linear Function 2 is $60.

Now we can summarize the initial values:

  • Linear Function 1: Initial value at \(x=0\) is $0.
  • Linear Function 2: Initial value at \(x=0\) is $60.

Based on these calculations, the comparison yields the following conclusion:

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.

So 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.