1. Rectangular Coordinate System
X-axis
Y-axis
(0,0)
Origin
Quadrant II
Quadrant I
Quadrant III
Quadrant IV

2. Rectangular Coordinate System
X-axis
Y-axis
(0,0)
Rectangular Coordinate System
(0,5)
(-5,4)
(1,3)
(6, -3)
(-2,-4)

3. Linear Equations in Two Variable
A linear equation in two variables is an equation of the form
Ax + By = C
where A, B, C are real numbers and A & B are both not zero
Examples of linear equation in two variables :
3x + 4y =23
X=6
7z + 4y =16
X + 9y = 0
The graph of any linear equation in two variables is a straight line

4. Solutions of Linear Equations in Two Variables
Example:
2x + y = 3
Some Solutions
Example:
y = 3x - 1
Some Solutions
x y
x y 3 -1 1 1 1 2 2 -1 2 5 -1 5 -1
- 4

5. Graphing Linear Equations in Two Variables5 4 3 2 1 -2 -3 -4 -5 y x
Graph:
2x + y = 3
(0, 3) 3 1 -1
x y 2 5
(1, 1)
(2, -1)

6. Graphing Linear Equations in Two Variables
The graph of 2x + y = 3 is a line.
The solution set of a linear equation in two variables is all the points that lie on the line of its graph 5 4 3 2 1 -2 -3 -4 -5 y x

7. X-intercepts and Y-intercepts
The x-intercept is the point where the line intersects the x-axis
What is the y-coordinate of the x-intercept?
The y-intercept is the point where the line intersects the y-axis
What is the x-coordinate of the y-intercept? 5 4 3 2 1 -2 -3 -4 -5 y x
2x + y = 3

8. Y - Intercepts The y – intercept is the y – value when x = 0.
When using a graph, the y – intercept is where the graph crosses the y – axis.
The y – intercept of the line to the right is …
To find the y-intercept, let x=0 in the given equation and solve for y. Then (0,y) is the y-intercept.

9. X - Intercepts The x – intercept is the x – value when y = 0.
When using a graph, the x – intercept is where the graph crosses the x – axis.
x – intercept is 2.
The x – intercept of the line to the right is …
To find the x-intercept, let y=0 in the given equation and solve for x. Then (x,0) is the x-intercept

10. y x Special Cases Graph: y = 3
This is the set of points that have a y-coordinate of 3.
(x, 3) for all x. 5 4 3 2 1 -2 -3 -4 -5 y x
The Graph of y= 3 is a horizontal line

11. y x Special Cases Graph: x = 5
This is the set of points that have a x-coordinate of 5.
(5, y) for all y. 5 4 3 2 1 -2 -3 -4 -5 y x
The graph of x= 5 is a vertical line

12. Graphing ax + by = c What about 3x + 4y = –12 ?
Step 1: Put equation in slope – intercept form
This means solve for y.
Step 2: Plot the y – intercept.
Step 3: Starting at the y – intercept, use the slope to find other points.
A slope of means
Down 3, Right 4…or…Up 3, Left 4 (the 3 or 4 can be negative, but not both).