#2**+1 **

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