Compare Linear Function 1 with Linear Function 2. Which one has the lesser initial value?

Question

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.

GPT-4o mini · Answer

To compare the initial values of the two linear functions, we can analyze them one by one.

Linear Function 1:

This function represents a constant cost: the cost is $45 per month. Therefore, the initial value (the cost when x = 0, which is the starting point) is $45.

Linear Function 2:

The equation given is $y = 40x + 60$. To find the initial value, we set $x = 0$: \[ y = 40(0) + 60 = 60. \] Thus, the initial value of Linear Function 2 is $60.

Comparison:

Linear Function 1 has an initial value of $45.
Linear Function 2 has an initial value of $60.

Thus, Linear Function 1 has the lesser initial value.

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.