Our class is learning about slopes and finding them (I am in 7th grade) and I seriously do not understand. A specific question is: The skiers are left off their lift at an elevation of 12,300 feet and have skied down to an elevation of 10,300 feet, and are 3,000 feet from an imaginary line that extends from the top of the mountain to it's base. The lift starts at an elevation of 4,000 feet to go up the mountain, which is where the ski slope ends. My teacher explains things very well, strangely, and if you could help me on this, just the general understanding, that would be great!
I would think of this problem as a big right triangle. Draw a triangle like this on your paper: /|
The slanted line should be labeled 10,300 feet at the bottom and 12,300 feet at the top. Think of this slanted line as how the skiers went down the mountain.
The line that's straight up and down is the height of the mountain (i.e. the "imaginary line that extends from the top of the mountain to it's base"). You don't know how high that is yet.
The line across the bottom (horizontal) is the 3,000 feet.
Now, what is the actual question? Do you need to find the slope of the part of the mountain the skiers skied on?
slope = rise / run OR slope = how far did you move vertically / how far did you move horizontally
Well, the skiers moved down the mountain from 12,300 to 10,300 feet. Subtract those and you get how far they moved vertically (i.e. the "rise"). This is also the height of your triangle (the part you didn't know yet from above). Remember, moving down is negative and moving up is positive.
Now, the horizontal movement is the distance from the skiers at the bottom of our triangle to the imaginary line coming down from the peak to the base. That information is given to you directly in the problem and that is your "run".