Algebra
4.1
Graphing Equations of Lines
The Coordinate Plane
y axis
VERTICAL
Origin (0,0)
x axis
HORIZONTAL
Quadrant II
( -, + )
Quadrant III
( -, - )
Quadrant I
( +, + )
Quadrant IV
( +, - )
Let’s check out plotting points
http://www.shodor.org/interactivate/
activities/GeneralCoordinates/
Equations in two variables, x and y
Consider the equation:
y = 2x + 3
There are an infinite number of combinations of x
and y that will make this equation true.
Each of these combinations is called an ordered
pair (x,y)
Each of these ordered pairs is called a solution of
the equation.
What is a solution?
How do you find the ordered pair?
y = 2x + 3
Choose a value for x and plug it in.
Let’s choose x = 2
y = 2(2) + 3
y = 7 So, when x = 2, y = 7
One solution to this equation is the ordered pair ( 2, 7 )
y = 2x + 3
What are some other solutions to
this equation?
•
What is y when x = 0 ?
y=3
So the ordered pair (0,3)
is one solution
•
What is y when x = 1 ?
y=5
So the ordered pair (1,5)
is another solution
•
What is y when x = -1 ?
So the ordered pair (-1,1)
is another solution
y=1
y
y = 2x + 3
x
y
2
7
1
5
0
3
-1
1
.
.
.
.
(2,7)
(1,5)
(0,3)
(-1,1)
x
y
y = 2x + 3
x
y
2
7
1
5
0
3
-1
1
.
.
.
.
(2,7)
(1,5)
(0,3)
(-1,1)
This is the graph of the equation y = 2x + 3
x
Graphing the Equation for a Line
using an X/Y Table
STEPS
1. Rewrite the equation in slopeintercept form ( y = mx + b)
2. Set up an x/y table and choose three
values for x (negative, 0, positive)
3. Plug in each x to compute each y
4. Plot the three ordered pairs (x,y)
5. Connect the points as a straight line
Graph:
y=
2
3
x-1
Hint: Choose values for x that are multiples of 3. This will make
it easier to compute y.
y
x
y
-3
-3
0
-1
6
3
.
(6,3)
.
.(0,-1)
(-3,-3)
x
Graph:
y=
2
3
x-1
Hint: Choose values for x that are multiples of 3. This will make
it easier to compute y.
y
x
y
-3
-3
0
-1
6
3
The 3 points connect in a line
.
(6,3)
.
.(0,-1)
(-3,-3)
x
Key Concepts
Every single point on a line
represents a combination of
(x, y) that makes the equation
true.
A line is a picture of all the
solutions to an equation.
Homework
Graphing W/S
Tuesday Math Lab or Lunch
A-Ariel, Kelly C.
2-Nhigel, Matt, Alyssa
3-Evan, Grace, Brett, Adam,
Seth, Andrew