Yasmin initially deposited $500 into a retirement account. She also deposits $100 per month into this account. The function used to determine the balance in Yasmin’s account is y=500+100x

Question

, with x
representing the number of months and y
representing the amount of money in the account at the end of every month. Graph the function to determine the amount Yasmin would have saved after 6 months and after 12 months. In 3–5 sentences, describe your graph, identify what Yasmin saved after 6 months and after 12 months, and explain what the graph of the function represents.(4 points)

Answer 1

To graph the function \( y = 500 + 100x \), you can plot the points corresponding to different values of \( x \) (number of months):

1. When \( x = 0 \) (the initial deposit), \( y = 500 + 100(0) = 500 \).
2. When \( x = 6 \) (after 6 months), \( y = 500 + 100(6) = 500 + 600 = 1100 \).
3. When \( x = 12 \) (after 12 months), \( y = 500 + 100(12) = 500 + 1200 = 1700 \).

Plotting these points alongside a few others, you would see a straight line starting at (0, 500) and increasing in a linear fashion.

The graph represents Yasmin's total savings in her retirement account over time. After 6 months, Yasmin would have saved $1,100, and after 12 months, she would have saved $1,700. The slope of the line indicates that she is adding $100 each month to her initial deposit of $500, resulting in a consistent, linear increase in her account balance.