Chapter 1.3, Problem 90E

Skills and Applications

Road Grade From the top of a mountain road, a surveyor horizontal measurements $y$, as shown in the table ( $x$ and $y$ are measured in feet).

$x$	300	600	900	1200
$y$	$-25$	$-50$	$-75$	$-100$

$x$	1500	1800	2100
$y$	$-125$	$-150$	$-175$

(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 indicated 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 $-\frac{8}{100}$. What should the sign state for the road in this problem?