Lines are often more complicated than simple vertical and
horizontal lines as we looked at in the last section. The
slopes of the lines we worked with so far were 0(perfectly horizontal) or
undefined(perfectly vertical.) However, there are an infinite number of
slopes in between these two extremes. We can find the slope of the line
between two points, and , with
the following equation:
For example, take the points (-2,1) and (5,4). We can see their location and the slope of the line connecting them.
Slope and y-intercept may
be found by manipulating an equation of a
into the form
The graph also shows two extremes in slopes. The green horizontal line is perfectly flat. The equation of that line is y = 3. Since there is no x term, the coefficient is understood to be 0. We can represent it with y = 0 * x + 3. The slope of the line is 0.
The yellow vertical line is represented by the equation x = -2. This line is not in the form y = mx + b because there is no y term. The slope on this line is undefined since the run of the line is 0, but the rise of the line is infinite.