Question

1. dave withdraws the same amount of money each week. dave started with $800 in his account. after 6 weeks of withdrawing money, he had $200 left in his account.

a. graph dave’s account balance as it changes over time. (put the points on the graph and draw the line. there is a straight - line tool to use! looks like a line with a dot on each end!)
b. what is the rate of change of dave’s withdrawal of money from his account. (hint: the rate of change is the same thing as the slope. use the slope formula to solve: $\frac{y_2 - y_1}{x_2 - x_1}$)
c. at this rate, how long will it take dave to run out of money? write the equation of the line in slope - intercept form and solve for x. hint: use 0 for y.)

Explanation:

Step1: Identify two points for graphing

The initial amount is $800 (at week 0), so the point is (0, 800). After 6 weeks, he has $200, so the point is (6, 200). Plot these points on the graph and draw a straight - line through them.

Step2: Calculate the rate of change (slope)

Let $(x_1,y_1)=(0,800)$ and $(x_2,y_2)=(6,200)$. Using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, we have $m=\frac{200 - 800}{6-0}=\frac{- 600}{6}=-100$. The rate of change of Dave's withdrawal is $100$ dollars per week.

Step3: Find the time to run out of money

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Here, $m=-100$ and $b = 800$, so the equation is $y=-100x + 800$. Set $y = 0$:
\[

$$\begin{align*} 0&=-100x+800\\ 100x&=800\\ x&=8 \end{align*}$$

\]

Answer:

a. Plot the points (0, 800) and (6, 200) and draw a straight - line through them.
b. The rate of change is $100$ dollars per week.
c. It will take 8 weeks for Dave to run out of money.