Need help using The Slope-Intercept Form?

Question

y=mx+b

Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth.

I would like how to do the equation and the answer. Please, I'm lost with this.

Answer 1

Slope = Change in Vert / Change in Horz

Slope = 1800 ft / 3.25 miles

3.25 miles (5280 ft / 1 Mile) = 17,160 Ft

Slope = 1800/ 17160 = 0.10489

Answer 2

Since you just need to find the slope, you are just calculating the 'm' part of the slope-intercept formula and don't need the rest for this problem.

Slope is "rise over run" which in this case would be -1800 ft / 3.25 mi. The rise is negative, because Tom is descending. There is no way to tell the sign of the run (horizontal direction), because it is not stated in the problem. We will assume that it is in the positive direction.

converting to ft:

(-1800 ft / 3.25 mi) * (1 mi / 5280 ft) = -0.104895.
Rounding to the nearest hundredth (2 decimal places) gives you -0.10.

Answer 3

Assume you start at point (0,0). Tom drives down the mountain and 3.25 mi down the road he is at an elevation of -1800 ft. Therefore, the second point becomes (3.25, -1800).

m = (y2-y1)/(x2-x1) = (-1800 - 0)/(3.25 - 0) = -553.8 ft/mi or .104 vertical ft for every horizontal foot.

This question only asks for the slope because it doesn't anchor you at any point in space. The graph can translate any way vertically or horizontally without changing the slope. So, it would be futile to try and use the point-slope form or the slope-intercept form.

Answer 4

y = mx + b

1800 = m x 3.25 x 5280 + b

Let us assume b = 0

m = 1800 / (3.25 x 5280) = 0.1049

m = tan theta and is the slope.

Answer 5

m = slope is height/base

change the units above to the same metric ft or mi

Answer 6

tangent x=slope
convert mile to feet or feet to mile
write similar formula
slope=1800/(3,25^2-1800^2)