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)
(
𝑥
)
and his total savings (y)
(
𝑦
)
is given by y=37x+40
𝑦
=
37
𝑥
+
40
(1 point)
Linear Function has the greater initial value.

Answer 1

To determine which linear function has the greater initial value, we first need to identify the initial values of both functions.

Linear Function 1:
Taesha's savings can be represented as:
\[ y = 25x + 50 \]
Here, the initial value (y-intercept) is \( 50 \) (when \( x = 0 \)).

Linear Function 2:
Joshua's savings is given by the equation:
\[ y = 37x + 40 \]
In this case, the initial value (y-intercept) is \( 40 \) (when \( x = 0 \)).

Comparison of Initial Values:

• Initial value of Linear Function 1 (Taesha): \( 50 \)
• Initial value of Linear Function 2 (Joshua): \( 40 \)

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

Therefore, the answer is: 1