Algebra help? Not understanding slopes :0(?

Question

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.
Thank you in advance.

Answer 1

slope is rise over run (vertical divided by horizontal)

rise = -1800 ft (negative because you went down)
run = 3.25 mi, = 17160 ft (there are 5280 ft in 1 mile)

-1800/17160 = -0.104895 = -0.105
(this tells us that for every 0.105 feet Tom descends, he goes 1 foot horizontally)

...i think i did that right

Answer 2

First things first, put everything into the same units of measure, in this case, change miles to feet. 3.25 mi x 5280 feet (in one mile) = 17160 feet.

I always draw a picture for these things, it keeps me from getting confused. Also, label all the information you have, including any (x,y) coordinates you can come up with. I drew an xy coordinate plain with the top of the mountain at the y- axis and the bottom of the mountain at the x-axis. I labeled the top of the mountain (1800, 0) and the bottom of the mountain (0, 17160).

As your other answerers stated before, slope= rise over run. The official formula for it is this:
y(2)-y(1) --- the numbers in parenthesis are subscripts
________ - line represents divided by, it's a fraction
x(2)-x(1)

So you fill the information you have into the equation, y(2) being the second y value, in this case 0, y (1) being the first y value, 1800. Then the x values, x(2) = 17160, x(1) = 0. This gives you:
0 - 1800 = -1800
_______ ______ = -.10489510 repeating
17160-0 = 17160

if you round that to the nearest hundredth it is -.10
since the four in the hundredths place is less than five.

If you put it into a linear equation, it will look similar to this:
y = -.10x + 1800
y= altitude, x= distance from the pinnacle, z= the altitude at which the pinnacle is at.

Therefore, the slope (-.10) tells us that for every .10 of a foot decended vertically(that is where the negative comes from - if you were ascending, the value of the slope would be a positive number) Tom moved one foot horizontally.

Answer 3

The answers before me gave you the right solution. I'll just add that slope is simply how steep the line is. So if you go down hills and cover a lot of altitude (rise) in very short distance (run), that's a steep hill. But if it takes a long distance to drop only a few feet, its not a steep hill. So take the altitude (rise) and divide by the horizontal distance (run) and that's the slope. Draw a picture to help you visualize the problem better.

Answer 4

the 2nd expression is in basic terms a statment announcing that 0= -one million+one million. there is no longer certainly one of those functional information in announcing that 0 = 0. y=one million/2x+one million is describing a line. A line with a slope of one million/2 (which skill it variations vertically 0.5 as quickly because it variations horizonally and it slopes in a favorable direction) and it occurs to circulate the Y axis at one million. You sparkling up the expresson by applying plugging in established values because you prefer to sparkling up for unknown values. that is in basic terms an intermediate step.

Answer 5

Remember: Slope = "Rise over Run".

Rise = **negative** 1800 ft.
Run = 3.25 miles * 5280 ft. = 17160 ft.

The slope would equal -1800/17160 ft. = (- 0.104895)

Looking over my answer, Heather did a better job of explaining it.

Answer 6

Either you need sierious help, or you don't pay any attention in class.