Determine the slope of the linear function represented by the following scenario:

Question

Jose opens a savings account with $150. He plans to save the $20 he earns each week mowing his neighbor's lawn.

Answer 1

To determine the slope of the linear function in this scenario, we need to identify what the slope represents.

In this case, the slope represents the rate at which Jose's savings increase over time. He earns a fixed amount of money ($20) each week from mowing lawns.

The function can be expressed in the form:

\[ S(t) = 150 + 20t \]

Where:

• \( S(t) \) is the total amount saved after \( t \) weeks,
• \( 150 \) is the initial amount saved (the y-intercept),
• \( 20 \) is the amount he saves each week (the slope),
• \( t \) is the number of weeks.

Therefore, the slope of the linear function is:

\[ \text{slope} = 20 \]

This means that for every week, Jose's savings increase by $20.

Answer 2

what is the y intecept

Answer 3

In the context of the scenario provided, the y-intercept represents the initial amount of money Jose has in his savings account before he starts saving more.

From the expression:

\[ S(t) = 150 + 20t \]

The y-intercept is the value of \( S(t) \) when \( t = 0 \) (which represents the initial amount before any additional savings).

At \( t = 0 \):

\[ S(0) = 150 + 20(0) = 150 \]

Thus, the y-intercept is:

\[ \text{y-intercept} = 150 \]

This means that when Jose opens the account, he starts with $150.