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)
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