Compare Linear Function 1 with Linear Function 2. Which one has the greater initial value? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.

Question

Linear Function 1: Taesha starts the year with $50 saved and then saves an additional $25 a week.
Linear Function 2: The relationship between the number of weeks Joshua has been saving (x) and his total savings (y) is given by y=37x+40


Linear Function ? has the greater initial value.

Answer 1

To compare the initial values of Linear Function 1 and Linear Function 2, we need to identify the initial value (the y-intercept) of each function.

Linear Function 1: Taesha starts the year with $50 saved and saves an additional $25 a week. The equation can be represented as: \[ y = 25x + 50 \] Here, the initial value (when \( x = 0 \)) is \( y = 50 \).

Linear Function 2: The function is given by: \[ y = 37x + 40 \] Here, the initial value (when \( x = 0 \)) is \( y = 40 \).

Now we can compare the initial values:

• Initial value of Linear Function 1 is $50.
• Initial value of Linear Function 2 is $40.

Since \( 50 > 40 \), Linear Function 1 has the greater initial value.

So, the answer is 1.