Graphing in Form y=mx + b
Graphing linear equations (equations without any exponents higher than
1) starts by putting the problem into the form y = mx + b
Here is an example:
y – 2x = 3
Move the –2x to the other side of the equation by adding it to
both sides. This becomes:
y = 2x + 3
Now you are ready to graph. Start by identifying the slope and y-intercept
of the equation. The slope is “m” in the formula. In this
problem, the slope is 2. The y-intercept is the “b” in the
formula. In this problem, the y-intercept is 3.
Start your graph by placing a point on the y-intercept. This is the place
where the line will cross the y axis. If the y-intercept is positive,
it will be on the upper half of the plane, if it is negative it will be
on the lower half. Here is what it will look like:
From the y-intercept, you will move whatever the slope designates. The
slope needs to be written as a fraction, in this case  .
Slope is defined as  .
This means, from the y-intercept you will “rise” the amount
in the numerator of the fraction, and “run” the amount of
the denominator. From (0,3) you will go up 2 and over 1. This takes you
to (1,5). Place a point here:
Now all you need to do is create your line by connecting the dots. Use
a straight edge.
Here is an example with a negative slope:
y = - 
+ 2
First, identify the slope (m) and y-intercept (b)
m = - ,
b = 2
Graph the y-intercept
From (0,2) you will go down 4, because the slope is negative,
and then over 3. When the slope is negative, the “rise” is
down. This puts you at (3, -2)
Now, connect the dots.
Horizontal Lines
Horizontal lines are a little different. A horizontal line will not
have an x value. Here is an example:
y = 4
In this case, the graph is a horizontal line through (0,4). The y-intercept
is 4, and the slope is 0.
Here is the graph:
Vertical Lines
Vertical Lines will not have a y value. The equation of a horizontal
line looks like this:
x = 4.
There is no y-intercept and the slope is undefined. The graph will be
a vertical line through (4,0). |
