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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 $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.

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.

1 answer

To compare the initial values of Linear Function 1 and Linear Function 2, let's analyze each function.

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

  • This can be interpreted as a linear function where the total cost (y) after x months can be represented as:
    \( y = 45x \)
    • Here, the initial value when \( x = 0 \) is \( y = 45(0) = 0 \).

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:
\( y = 40x + 60 \)

  • In this equation, when \( x = 0 \):
    \( y = 40(0) + 60 = 60 \)
    • Thus, the initial value for Linear Function 2 is 60.

Now, we compare the initial values:

  • Linear Function 1 has an initial value of \( 0 \).
  • Linear Function 2 has an initial value of \( 60 \).

From our comparison, Linear Function 1 has the lesser initial value of \( 0 \) while Linear Function 2 has an initial value of \( 60 \).

Thus, the correct statement 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.