236CHAPTER15 Graphs of Linear Relations
We’ve seen the graphs of some relations and functions. Now it’s time to focus on the graphs of
linear relations. These always appear as straight lines in the Cartesian plane. In particular, we’re
interested in the equations and graphs of linear functions—linear relations where the straight-
line graph is not vertical (that is, not parallel to the dependent-variable axis).Slope-Intercept Form
One of the best known ways to relate the graph of a linear function with its equation
defines the slope of the line and the point where it crosses the dependent-variable axis.
Atwo-variable linear equation of this sort is said to be in slope-intercept form. Let’s call it the
SI form for short.What is slope?
The slope of a straight line in the Cartesian plane is an expression of the steepness with which
the line ramps upward or downward as we move to the right. A horizontal line has a slope of 0. A
line that ramps upward as we move to the right has positive slope that increases without limit
as the slant angle approaches 90° (vertical and going straight up). If the line ramps down as
we move to the right, the slope decreases from 0, becoming more negative without limit as the
slant angle approaches −90° (vertical and going straight down).
To figure out the exact slope of a line in the Cartesian plane, we must know the
coordinates of two points on that line. These can be any two points, as long as they’re
different. The slope of a line passing through two points is equal to the difference in
they values divided by the difference in the x values for the points. In this context,
mathematicians abbreviate “the difference in” by writing the uppercase Greek letter delta (Δ).
These differences are often called increments. The slope of a line is usually symbolized as m.
Therefore,m=Δy/ΔxCopyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use.