**Find the slope of a line given two points on the line**

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To obtain a formal definition of the slope of a line, we designate two different points on the line. To differentiate between the points, we write them as (x_{1} , y_{1}) and (x_{2} , y_{2}). See Figure (The small numbers 1 and 2 in these ordered pairs are called *subscripts. *Read (*x*1, *y*1) as “*x*-sub-one, *y*-sub-one.”) (*x*1, *y*1) and (*x*2, *y*2).

As we move along the line in Figure from (*x*1, *y*1) to (*x*2, *y*2), the *y*-value changes (vertically) from *y*1 to *y*2, an amount equal to *y*2 – *y*1. As *y *changes from *y*1 to *y*2, the value of *x *changes (horizontally) from *x*1 to *x*2 by the amount *x*2 – *x*1. The ratio of the change in *y *to the change in *x *(the rise over the run) is called the *slope *of the line, with the letter *m *traditionally used for slope.

**Slope Formula**

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The **slope **of the line through the distinct points (*x*1, *y*1) and (*x*2, *y*2) is

(x_{1 }≠ x_{2}).