Question

consider the graph to the right.
a. in words, describe the function shown on the graph.
b. find the slope of the graph and express it as a rate of change.
c. briefly discuss the conditions under which a linear function is a realistic model for the given situation.

a. according to the function, the distance from home increases by 700 miles every 8 hours.
b. according to the function, the distance from home increases by 8 miles every 700 hours.
c. according to the function, the distance from home decreases by 700 miles every 8 hours.
d. according to the function, the distance from home decreases by 8 miles every 700 hours.

b. calculate the slope of the graph and express it as a rate of change.
rate of change =
(round to the tenths place as needed.)

Explanation:

Identify variables and initial values

Using the Independent and Dependent Variables and Graph Interpretation knowledge points

• The horizontal axis represents time in hours, \(t\).
• The vertical axis represents distance from home in miles, \(d\).
• The vertical intercept is at \((0, 700)\), meaning the initial distance from home is \(700\text{ miles}\).
• The horizontal intercept is at \((8, 0)\), meaning the distance becomes \(0\text{ miles}\) after \(8\text{ hours}\).

Describe the function in words

Using the Graph Interpretation knowledge point

• Since the line starts at \(700\text{ miles}\) and decreases to \(0\text{ miles}\) over \(8\text{ hours}\), the distance from home decreases by \(700\text{ miles}\) every \(8\text{ hours}\).
• This matches option C.

Calculate the slope of the graph

Using the Rate of Change Interpretation knowledge point

$$ \text{Slope} = \frac{d_2 - d_1}{t_2 - t_1} = \frac{0 - 700}{8 - 0} = \frac{-700}{8} = -87.5 $$

Express as a rate of change

Using the Rate of Change Interpretation knowledge point

• The rate of change is the slope of the line, which is \(-87.5\text{ miles per hour}\).
• This represents a decrease in distance of \(87.5\text{ miles}\) per hour.

Answer:

Question 1

• A. According to the function, the distance from home increases by 700 miles every 8 hours.
• B. According to the function, the distance from home increases by 8 miles every 700 hours.
• C. According to the function, the distance from home decreases by 700 miles every 8 hours. (Correct answer)
• D. According to the function, the distance from home decreases by 8 miles every 700 hours.

Question 2

rate of change = <blank>-87.5</blank> miles per hour