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Properties of Functions Quick Check
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Question
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 $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.
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 $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.

1 answer

To determine which linear function has a lesser initial value, we need to consider the initial values (y-intercepts) of both functions.

  1. Linear Function 1: Lionel’s cell phone plan costs $45 per month.

    • This can be interpreted as a function where the cost is a constant $45. The initial value (y-intercept) is therefore $45.

  2. Linear Function 2: The relationship is given by \(y = 40x + 60\).

    • In this linear function, the initial value (y-intercept) is the constant term, which is $60 (when \(x = 0\)).

Now, comparing the initial values:

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

Since $45 is less than $60, Linear Function 1 has the lesser initial value.

Therefore, 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.