Chapter — Graphng
Equations in two variables are classified by the exponent (power) of the variables. First degree equations,
that is, equations whose variables are raised to the first power, are
. That means that
when these equations are graphed in the Rectangular Coordinate System, their graphs make a straight
Linear equations fit a pattern that looks like Ax + By = C, where x and y are the variables and A, B, and C
are real number constants with A and B not both equal to zero. Ax + By = C is called the
equation of a line.
For example, the equation 2x + 3y = 10 is a linear equation
with infinitely many solutions; (2, 2), (5, 0), and (–1, 4)
are just a few of them. You can see from the graph of this
line (the figure at right) that solutions to a linear equation
are points on the graph of that equation.
x and y-Intercepts
There are two
ordered pair solutions
extra information and that have special names, the x- and
is the point at which the
graph of the line crosses the x-axis. As you can see in the
figure at right, that point is (5, 0). It is important to note
that the y-coordinate of this point is zero. Similarly, the
is the point at which the graph of the line
crosses the y-axis. The x-coordinate at this point is zero. Though we have not plotted this point on the
graph of the line, you can see that it does exist at the point where the line crosses the y-axis.
The x and y-intercepts allow us to find two ordered pair solutions with minimal effort.
The point at which the line crosses the x-axis is the x-intercept at (x, 0).
The point at which the line crosses the y-axis is the y-intercept at (0, y).
y = mx + b: The Slope-Intercept Form of the Equation of a Line
There is a special form of the equation for a line that allows us to read information directly from it. The
for the equation of a line looks like y = mx + b. From the slope-intercept form
of an equation, we can determine two important pieces of information by inspection—just by reading the
The first is m, the coefficient of x. That value has special meaning
for the graph of the line. It is the
of the line, or how steep
or inclined the line is. The value b in the slope-intercept form
indicates the second piece of information, the y-intercept, which
is the point (0, b).