Question

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. 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

Answer 1

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

Linear Function 1: Taesha starts the year with $50 saved. This indicates her initial value is:

• Initial Value (y-intercept) = $50

Additionally, she saves an additional $25 a week, but the initial amount is what we need for the comparison.

Linear Function 2: The relationship is given by the equation \( y = 37x + 40 \). In this equation, the y-intercept (initial value) is indicated by the constant term when \( x = 0 \):

• Initial Value = $40

Comparison:

• Linear Function 1 has an initial value of $50.
• Linear Function 2 has an initial value of $40.

Since $50 (Linear Function 1) is greater than $40 (Linear Function 2), the conclusion is:

Choose 1 for Linear Function 1.