Graphing Linear Equations
Objective Learn to recognize linear equations
and to graph them by plotting points by hand.
The most important objective in this lesson is that you
practice graphing lines by hand. This process is important
because it helps increase your understanding of what the graphs
mean and how the graphs depend on the coefficients in the linear
The class of equations that have straight lines as graphs is
called the class of linear equations, and that
this class can be described algebraically.
Key Idea A linear equation can always be
written in the form 2
Ax + By = C .
The equations 2x - 5y = 7, 3x + 5y = -1, and -4x + 7y = 11 are
all linear equations.
Note that the form in the key idea is only one form in which
linear equations may be expressed. Equations not in the Ax + By =
C form are still linear because they can be rewritten in this
form by using the Addition and Multiplication Properties of
Equality. Besides, not all equations are given using the
variables x and y. When other variables are used, it is important
to specify which variable corresponds to the horizontal axis and
which corresponds to the vertical axis.
The equation d = 3 t is linear. It can be rewritten as - 3t +
d = 0 by subtracting 3t from each side of the equation. This
equation is in the Ax + By = C form, with t playing the role of x
and d playing the role of y .
The equation y = -4 x + 1 is linear. By adding 4x to each
side, it can be rewritten as 4 x + y = 1.
For an equation in the Ax + By = C form, it is usually best to
solve for y in terms of x in order to plot points.