Graphing Linear Equations
A linear equation producing the graph of a line is an equation
in two variables (most often x and y) where both variables are to the first
degree. The standard form is Ax + By = C, where A, B, and C are
Integers and A > 0 (in other words A is positive.) Graphing lines may be accomplished using one of several methods. The goal is to find three
co-linear points to determine a given
line. The easiest method is
the slope-intercept method.
A linear equation is an equation which would produce the graph of
a line. Solving the equation for y would produce the slope-intercept equation of the
line. The form of this line would then be
,
where m is the slope and b is the y-intercept. Once the line is in this
form, recognize the coefficient of the x (the number in front of the x) as the slope and
the constant number (the number that is not in front of a either variable) as the
y-intercept.
The following example shows how to solve a linear equation for the
variable y:
Solve the equation
for y.
…subtract
2x from both sides, notice that the x term is 1st
…divide all terms by
…the slope of the line is
and the y-intercept is
…which means m =
, and b = (0,-4)
The line could then be easily graphed by first plotting the
y-intercept which is “b”. Think of “b” as the beginning point to plot for the line; it is
on the y-axis. The y-intercept (or
“b”) is the point (0,b) and for the example above that point would be (0, -4). Next using the slope, plot two additional points. Since m =
think of “m” as how to move to the next point from the y-intercept. The numerator (top number) of the slope tells how many units to move vertically (up or down depending on whether the number is positive
or negative) and the denominator (bottom number) of the slope tells you how many units to
move horizontally (right or left depending on whether the number is positive or negative). Since the slope in the example above is
,
then from (0,-4) move up two units
and to the right 3 units, plotting the point (3,-2). Moving another 2 units up and 3 units
to the right, plot the third point (0,6). Now
that three co-linear points have been plotted, using a straight-edge draw a line through the points
with arrows at the ends of the line indicating that there are many points (solutions) on
that particular line.