SOLUTION: Road Gradient Driving down the smoky mountains in Tenn. Sam finds that she decends 2000 feet in elevation during the time that she has moved 4 miles horizontally away from a high p

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Question 158574: Road Gradient Driving down the smoky mountains in Tenn. Sam finds that she decends 2000 feet in elevation during the time that she has moved 4 miles horizontally away from a high point on the straight road. Find the slope (gradient) of the road (1 mile+5280 feet)
Please help I am stumped on how the equation should be wriiten in order to have it solved! Thanks so much
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
it looks like what they are looking for is a change in the vertical direction divided by the change in the horizontal direction.
if you let y = vertical direction and x = horizontal direction, then change in vertical direction divided by change in horizontal direction is the slope.
so change in vertical direction is given by the equation y2-y1 = change in vertical direction.
change in the horizontal direction is given by the equation x2-x1 = change in horizontal direction.
slope is y2-y1/x2-x1
y1 = 2000 (her starting elevation in feet
y2 = 0 (her finishing elevation
x1 = 0 (her starting horizontal miles
x2 = 4 (her finishing horizontal miles
formula then becomes
y2-y1 = 0 - 2000 = (-2000) feet
x2-x1 = 4 - 0 = 4 miles
(y2-y1)/(x2-x1) becomes
-2000/4 = -500 feet per mile.
if you were to graph this, you would use the slope intercept form of the general equation y = m*x + b, where m is the slope and b is the y intercept when x = 0.
x represents horizontal direction in miles
y represents elevation in feet
the slope is -500/feet per mile
when x is 0, y is 2000 (given) so b is 2000 which is the y-intercept.
formula then becomes
y - -500*x+2000
the graph of this equation would look like this:

as you can see, when x = 0 miles, elevation is 2000 feet, and when x = 4 miles, elevation is 0 feet.