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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 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 $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 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.

1 answer

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

Linear Function 1: The cost of Lionel's cell phone plan is given as a flat rate of $45 per month. This means that regardless of the number of months, the initial subscription cost (when x = 0 month) 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 represented by the equation \( y = 40x + 60 \). Here, the initial value is the y-intercept of the function. When x = 0 (the starting point), the cost is: \[ y = 40(0) + 60 = 60. \] So, the initial value for Linear Function 2 is $60.

Now let's compare the two initial values:

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

Conclusion: Linear Function 1 has the lesser initial value, which is $45, while Linear Function 2 has an initial value of $60.

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.