Question

1. the graph at the right shows the amount in a savings account over the course of 50 weeks.

what is the average rate of change? include units in your answer. explain in words what the rate of change means for the given situation.
step 1 find the coordinates of the x - and y - intercepts.
· x - intercept (50,0)
· y - intercept (0,500)
step 2 use the slope formula to find the average rate of change between the intercepts: slope = \\( \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\\)______ =

Explanation:

Step1: Identify the coordinates

The \(x -\) intercept is \((50,0)\) and the \(y -\) intercept is \((0,500)\). Let \((x_1,y_1)=(50,0)\) and \((x_2,y_2)=(0,500)\).

Step2: Apply the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substitute the values: \(m=\frac{500 - 0}{0 - 50}=\frac{500}{- 50}=-10\).

The units of the average rate of change are dollars per week.

The rate of change means that the amount of money in the savings account is decreasing by \(10\) dollars per week.

Answer:

The average rate of change is \(- 10\) dollars per week. It means the amount of money in the savings account is decreasing by \(10\) dollars each week.