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# how to find gradient of a line

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how do i find the gradient of a line?

Guest Aug 6, 2017
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y2-y1 / x2-x1

Guest Aug 6, 2017
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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:

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