Functions Worksheet - Big Ideas Math Prealgebra: A Florida Standards Curriculum Teaching Edition Page 21
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47Real-Life Application
3 3
EXAMPLE
You are controlling an unmanned aerial vehicle (UAV) for
Height
Minutes,
surveillance. The table shows the height y (in thousands of feet) of
(thousands
x
the UAV x minutes after you start its descent from cruising altitude.
of feet), y
0
65
a. Write a linear function that relates y to x. Interpret the slope and
10
60
the y-intercept.
20
55
You can write a linear function that relates the dependent variable
30
50
y to the independent variable x because the table shows a constant
rate of change. Find the slope by using the points (0, 65) and (10, 60).
60 − 65
− 5
change in y
m =
=
=
= − 0.5
—
—
—
10 − 0
change in x
10
Common Error
Because the line crosses the y-axis at (0, 65), the y-intercept is 65.
Make sure you consider
So, the linear function is y = − 0.5x + 65. The slope indicates
the units when
that the height decreases 500 feet per minute. The y-intercept
interpreting the slope
indicates that the descent begins at a cruising altitude
and the y-intercept.
of 65,000 feet.
b. Graph the linear function.
UAV Flight
Plot the points in the table and
y
draw a line through the points.
80
70
Because time cannot be negative
y
0.5x
65
60
in this context, use only positive
50
values of x.
40
30
20
10
0
0
10
20
30
40 50
60
70
80
x
Minutes
c. Find the height of the UAV when you stop the descent after 1 hour.
Because 1 hour = 60 minutes, fi nd the value of y when x = 60.
y = − 0.5x + 65
Write the equation.
= − 0.5(60) + 65
Substitute 60 for x.
= 35
Simplify.
So, the descent of the UAV stops at a height of 35,000 feet.
3.
WHAT IF?
You double the rate of descent. Repeat parts (a)–(c).
Exercises 11–13
Section 6.3
Linear Functions
259
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