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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 $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 $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 $40.

1 answer

To compare the initial values of the two linear functions, we need to determine the y-intercept (initial value) of each function.

Linear Function 1: Lionel’s cell phone plan costs $45 per month. This function can be expressed as:

  • \( y = 45x \)
  • The initial value (when \( x = 0 \)) is \( 0 \).

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:

  • \( y = 40x + 60 \)
  • The initial value (when \( x = 0 \)) is \( 60 \).

Comparison:

  • Linear Function 1's initial value: \( 0 \)
  • Linear Function 2's initial value: \( 60 \)

Thus, Linear Function 1 has the lesser initial value of \( 0 \) 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 $0 while Linear Function 2 has an initial value equal to $60.