ROAD GRADE From the top of a mountain road, a surveyor takes...

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 instance, a surveyor would put up a sign that states "$8\%$ grade" on a road with a downhill grade that has a slope of $-\frac{8}{100}$. 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 instance, a surveyor would put up a sign that states "$8\%$ grade" on a road with a downhill grade that has a slope of $-\frac{8}{100}$. What should the sign state for the road in this problem?

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