Question

To become a member at a local nature preserve, applicants must pay an initiation fee of $50 plus their yearly membership dues, as shown in the graph. What is the slope of the line joining these points, and what does the slope represent?

Answer 1

The line obtained by joining the points must pass through points (2,300) and (6,800).

The slope of line passing though point (x_1,y_1) and (x_2,y_2) is,

`m=(y_2-y_1)/(x_2-x_1)`

So slope of line passing through the point (2,300) and (6,800) is,

`\begin{gathered} m=(800-300)/(6-2) \\ =(500)/(4) \\ =125 \end{gathered}`

So slope of line is 125.

The slope of line give rate of change in y-coordinate for unit change in x-coordinate. In the given graph y-axis represent total cost and x-axis represents the years of memebership.

So slope represents the increase in total cost for unit increase in year of membership, or slope represents cost of one year membership.