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?

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25-10-2022
Mathematics

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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?

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ChelseaZ163877 ChelseaZ163877 · Answer 1 · 2022-10-25T21:55:39+02:00

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,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

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

[tex]\begin{gathered} m=\frac{800-300}{6-2} \\ =\frac{500}{4} \\ =125 \end{gathered}[/tex]

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.