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how do i find the gradient of a line?

Guest Aug 6, 2017
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 #1
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y2-y1 / x2-x1

Guest Aug 6, 2017
 #2
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The gradient (usually referred to as the slope) of a line indicates its steepness. There is an equation that allows one to calculate the gradient. It is the following:

 

\(m=\frac{y_2-y_1}{x_2-x_1}\)

 

m = slope of line

 

Before we can understand this equation, let's try putting it to use on some lines:

 

Source: http://www.coolmath.com/sites/cmat/files/images/06-lines-01.gif

 

Let's use this line and the points designated on the line to figure out its slope:

 

\(m=\frac{y_2-y_1}{x_2-x_1}\)Plug in the appropriate value for the y-coordinates and the x-coordinates.
\(m=\frac{3-(-1)}{4-(-2)}\)Simplify the numerator and denominator by recognizing that subtracting a negative is equivalent to adding a positive.
\(m=\frac{3+1}{4+2}\) 
\(m=\frac{4}{6}\)When finding the gradient, you should simplify it into simplest terms
\(m=\frac{2}{3}\) 
  

 

It does not matter which order you subtract the y-coordinates, but make sure that you subtract them in the same order as your x-coordinates. Otherwise, your slope will be incorrect.

TheXSquaredFactor  Aug 6, 2017

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