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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 $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.

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.

1 answer

To compare the initial values of the two linear functions:

Linear Function 1: Lionels's cell phone plan costs $45 per month. This implies that every month, regardless of the number of months, the cost will always start at $45.

Linear Function 2: The relationship is given by \( y = 40x + 60 \). To determine the initial value, we can substitute \( x = 0 \) (which represents the starting point when Ruby hasn't had her cell phone plan for any months yet):

  • When \( x = 0 \): \[ y = 40(0) + 60 = 60 \]

So, the initial value of Linear Function 1 is $45, and the initial value of Linear Function 2 is $60.

Comparing these values, we find:

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

Thus, 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.