The slope is the constant
rate of change of a linear function. It can be though of as the ratio
of the vertical change to the horizontal change between two points
on the graph of a line. If the two points are (x1,
y1) and (x2, y2), then the vertical
change is y2 - y1 and the horizontal change
is x2 - x1. Hence we can use the formula
to determine the slope
of a line if we know two points on that line. See Figure 1 below.
the following interactive example to see how the slope of a line is
computed when two points are known. What observations can you make?
In general, when the slope
of a linear function is positive, the function will be increasing.
That is, the graph will be a line that rises from left to right. When
the slope is negative, the function will be decreasing and the graph
will be a line that falls from left to right. If the slope of a linear
function is 0, then the function is neither increasing nor decreasing,
but is constant. The graph of a constant function is a horizontal
the next interactive example to see how different values of the slope,
m, affect the graph of the linear function y = mx + b.