Question

A sand dune stands 5 feet above sea level. The hill is eroding at a rate of 1 foot per 20 years. Let y represent the height of the sand dune after x years. Which equation represents the situation?

Answer 1

`y=-(1)/(20)x+5`

Explanation:

Here we are given that the present height of the sand dune is 5 ft and it is eroding 1 ft in every 20 years. If x represent the number of years and y represents the height of the sand dune. Hence we can consider the coordinates be (0,5) (20,4) (40,3) (60,2) (80,1) (100,0)

Let us evaluate the equation of the line plotted on these coordinates

Here we can see the y intercept is 5

Let us find the slope

`m=(y_2-y_1)/(x_2-x_1)\\m=(5-4)/(0-20)\\m=(1)/(-20)\\m=-(1)/(20)`

The equation in slope intercept form is given as

y=mx+c

where c is y intercept i.e. 5

`y=-(1)/(20)x+5`

Hence this is our required equation