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A group of volunteers is spending a week
cleaning up the trails in the Hudson Highlands.
On day 2 the volunteers begin at the point on the
trail where they ended the day before. The graph
shows their elevation, in feet, as a function of the
number of hours they work to clean the trails.
Elevation (ft)
800
O1 2 3 4 5 6 7 8
Time (h)
a. What does the ordered pair (1, 1000) on the graph represent?
b. The graph begins at 720 on the y-axis. What does this value represent? Is this
the rate of change or the initial value?
c. By how many feet does the elevation increase for one hour of work? What does
this value represent, rate of change or initial value?
d. What is the equation that represents this function?

a. after 1 hour they were at 1000 ft of elevation.

b. initial value

c. rate of change

d. y = 280*x + 720

Step-by-step explanation:

In the figure attached, the graph is  shown.

a. The ordered pair (1, 1000) means that after 1 hour they were at 1000 ft of elevation.

b. 720 is the initial value, that is, the value when t = 0

c. From t = 0 to t = 1 the elevation goes from 720 ft to 1000 ft, then, in 1 hour their elevation increase 1000 - 720 = 280 ft. It represents the rate of change

d. Using the slope-intercept form:

y = m*x + b

where m is the slope (or rate of change in a linear equation like in this problem) and b is the y-intercept (referred previously as the initial value for the context of this problem). Replacing with the obtained values:

y = 280*x + 720

where y is the elevation (in feet) and x is time (in hours)