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7/27/2019 How to find the slope.docx
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How to find the slope
Here is how to find the slope. We saw in the lesson aboutwhat is slopethat slope is a measure ofhow steep a line is
That steepness can be measured with the following formula:
Let's illustrate this with an example:
For this situation, we see that the rise is 2 and the run is 4, so slope = 2/4
slope = 1/2 after simplification
what is the meaning of 1/2 ?
Since 1/2 is positive, you are going uphill. Now, suppose the unit is yard
1 is the rise. 2 is the run. This means that everytime you go up 1 yard, you go accross or horizontally2 yards
This situation is not very steep. However, take a look at the following:
http://www.basic-mathematics.com/what-is-slope.htmlhttp://www.basic-mathematics.com/what-is-slope.htmlhttp://www.basic-mathematics.com/what-is-slope.htmlhttp://www.basic-mathematics.com/what-is-slope.html7/27/2019 How to find the slope.docx
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Here, the rise is 8 and the run or horizontal distance is 2
So, slope = 8/2 = 4 meters
4 meters = 4/1 meters. This means that each time you go 4 meters straight up, you only go 1 meterhorizontally
This situation is very steep because you go up a lot compared to going horizontally
Now, let's see how to find the slope when we don't know the rise and the run.
If we graph the slope on the coordinate system, we will be able to derive another useful formula
Let us then try to put a slope of 8 as in previous example on the coordinate system.
Put a rise of 8 anywhere you wish. Then, put a run of 2. Here we go!
7/27/2019 How to find the slope.docx
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Draw the slope (in red)
If we remove everything in blue( rise and run), you are left with just the slope of the line
. Then, label the two endpoints with their respective coordinates
7/27/2019 How to find the slope.docx
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The two coordinates (4, 9) and (2,1) can be used to get a slope of 4
Notice that 9 1 = 8. But 9 and 1 represent y-coordinates
Since we cannot call both coordinates y, we can call one y1 and call the other y2
Let y1 = 9
Let y2 = 1
Therefore, 9 1 = y1 y2 = 8 = rise
Notice also by the same token that 4 2 = 2. But 4 and 2 represent x-coordinates
Since we cannot call both coordinates x, we can call one x1 and call the other x2
Let x1 = 4
Let x2 = 2
Therefore, 4 2 = x1 x2 = 2 = run
We can see then that
y1 y2 = rise and
x1 x2 = run
The formula becomes:
So, if the rise and the run are not given, but you know at least two points, use the formula right
above
Examples: How to find the slope when points are given
1) (8, 8) and (4, 4)
Let (x1,y1) = (8, 8) and (x2,y2) = (4, 4)
(y1 y2) / (x1 x2) = (8 4 )/(8 4 ) = 4/4 = 1
Since 1 is positive, the line goes up as you move from left to right
2) (1, -5) and (2, -10)
Let (x1,y1) = (1, -5) and (x2,y2) = (2, -10)
7/27/2019 How to find the slope.docx
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(y1 y2) / (x1 x2) = (-5 -10 )/(1 2) = (-5 + + 10)/-1 = 5/-1 = -5
Since -5 is negative, the line goes down as you move from left to right
Notice that
(y2 y1) / (x2 x1)= (-10 -5 )/(2 1) = (-10 + + 5)/1 = -5/1 = -5
In general slope = (y1 y2) / (x1 x2) = (y2 y1) / (x2 x1)
Now don't you wonder anymore about how to find the slope!