Road Grade From the top of a mountain road, a surveyor takes several horizontal measurements x and several vertical measurements y , as shown in the table ( x and y are measured in feet). (a) Sketch a scatter plot of the data. (b) Use a straightedge to sketch the line that you think best fits the data. (c) Find an equation for the line you sketched in part (b). (d) Interpret the meaning of the slope of the line in part (c) in the context of the problem. (e) The surveyor needs to put up a road sign that indicates the steepness of the road. For example, a surveyor would put up a sign that states “ 8 % grade ” on a road with a downhill grade that has a slope of − 8 100 . What should the sign state for the road in this problem?
Road Grade From the top of a mountain road, a surveyor takes several horizontal measurements x and several vertical measurements y , as shown in the table ( x and y are measured in feet). (a) Sketch a scatter plot of the data. (b) Use a straightedge to sketch the line that you think best fits the data. (c) Find an equation for the line you sketched in part (b). (d) Interpret the meaning of the slope of the line in part (c) in the context of the problem. (e) The surveyor needs to put up a road sign that indicates the steepness of the road. For example, a surveyor would put up a sign that states “ 8 % grade ” on a road with a downhill grade that has a slope of − 8 100 . What should the sign state for the road in this problem?
Solution Summary: The author plots the scatter plot for the data of several horizontal and vertical measurements taken by a surveyor from the top of the mountain road.
Road Grade From the top of a mountain road, a surveyor takes several horizontal measurements
x
and several vertical measurements
y
,
as shown in the table (
x
and
y
are measured in feet).
(a) Sketch a scatter plot of the data.
(b) Use a straightedge to sketch the line that you think best fits the data.
(c) Find an equation for the line you sketched in part (b).
(d) Interpret the meaning of the slope of the line in part (c) in the context of the problem.
(e) The surveyor needs to put up a road sign that indicates the steepness of the road. For example, a surveyor would put up a sign that states
“
8
%
grade
”
on a road with a downhill grade that has a slope of
−
8
100
.
What should the sign state for the road in this problem?
Formula Formula Point-slope equation: The point-slope equation of a line passing through the point (x 1 , y 1 ) with slope m , is given by the following formula: y - y 1 = m x - x 1 Example: The point-slope equation of a line passing through (2, -6) with slope 5 is given by: y - (-6) = 5(x - 2) y + 6 = 5(x - 2)
Listen
A falling object travels a distance given by the formula d = 6t + 9t2 where d is in feet
and t is the time in seconds. How many seconds will it take for the object to travel
112 feet? Round answer to 2 decimal places. (Write the number, not the units).
Your Answer:
Solve by the quadratic formula or completing the square to obtain exact solutions.
2
e
104
OA) -16±3√6
B) 8±√10
O c) -8±√10
OD) 8±3√√6
U
Question 14 (1 point)
Listen
The frame on a picture is 18 in by 22 in outside and is of uniform width. Using
algebraic methods, what is the width of the frame if the inner area of the picture
shown is 250 in²2? Write answer to 2 decimal places. (Write the number with no
units).
18 in
Your Answer:
22 in
Chapter 2 Solutions
College Algebra Real Mathematics Real People Edition 7
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