Question

regan and her family take a day trip to the beach at coral cove. their distance from the beach decreases the longer they drive.
this situation can be modeled as a linear relationship.
complete the statement that describes the situation.
regan’s family starts __ miles away from coral cove. the distance the family is from coral cove decreases by __ miles every hour.

Explanation:

Step1: Find the initial distance

The y - intercept of the linear graph (when \(x = 0\), time driving is 0 hours) gives the initial distance. From the graph, when \(x = 0\), \(y=200\). So the family starts 200 miles away from Coral Cove.

Step2: Calculate the rate of decrease (slope)

The slope \(m\) of a line is given by \(\frac{y_2 - y_1}{x_2 - x_1}\). We can take two points, say \((0,200)\) and \((2,80)\) (from the graph, when \(x = 2\) hours, \(y = 80\) miles).
\(m=\frac{80 - 200}{2-0}=\frac{- 120}{2}=- 60\). The negative sign indicates a decrease, so the distance decreases by 60 miles every hour.

Answer:

Regan’s family starts \(\boldsymbol{200}\) miles away from Coral Cove. The distance the family is from Coral Cove decreases by \(\boldsymbol{60}\) miles every hour.