# 2.1 Graphs and Graphing Utilities ```3.1 Graphing
The Rectangular Coordinate System
x-axis
origin
y-axis
• Each point in the coordinate system corresponds
to an ordered pair (x,y)
• Example: (3,5)
• The first number is called x-coordinate and the
second number is called y-coordinate
(3,5)
Plotting Points
• When you plot the points,
always look for the
numbers on the x-axis
(horizontal line) first:
negative # is on the left,
positive is on the right,
then move up (if +) or
move down (if -)
• Ex: Plot (-2,3)
And (0, -4)
(-2, 3)
(0, -4)
More examples
•
•
•
•
•
•
•
•
(1, 5)
(-4, -4)
(-1, 3)
(6,0)
(0, 2)
(3/2,3)
(4, -5)
(0, -3)
Graphing equations
• Steps
– Create a table with x and y
– Give x at least 3 values if it is a linear equation,
if not, give x at least 5 values
– Find y
– Form ordered pairs
– Plot the ordered pairs
– Connect the graph
Example 1
• Graph y = 2x + 1
x
-2
y = 2x + 1
&raquo;
Y = 2(-2)
+ 1 = -4 + 1 = -3
0
Y = 2 &raquo;(0) + 1 = 0 + 1 = 1
(0, 1 )
2
Y = 2(2)
+1 = 4+1=5
&raquo;
(2, 5 )
(-2, -3)
Continue…
Y=2x +1
Order
pairs
(-2,-3)
(0,1)
(2,5)
• Y = (1/2)x + 2
For equation with fractions, what numbers
should we choose for x?
```