Slope Of a Line

Slope if a Line

An important characteristics of a straight line is its slope, a number that represents the “steepness” of the line. To see how slope is defined, look at the line in Figure. The line goes through the points  (x_x ,y₁) = (-3,5) and  (x₂ , y₂) = (2 , -4). The difference in the two x – values,

x₂ – x₁ = 2 – (-3) = 5

in this example, is call the change in x. The symbol x (read “delta x”) is used to represent the change in x. In the same way, y represents the change in y.

In our example

y = y₂ – y₁

= -4 – 5 = -9.

These symbols, x and y, are used in the following definition of slope.

Slope Of a Line

The slope of a line is defined as the vertical change (the “rise”) over the horizontal change (the “run”) as one travels along the line. In symbols, taking two different point  and  on the line, the slope is

m =  , where