1. 1. Place your test corrections in the blue folder
Thurs, 9/15
SWBAT… review the Cartesian Coordinate system & graph linear equations using a table of values
Agenda
WU (10 min)
Brain Pop video – Cartesian Coordinate System (10 min)
Notes on linear equations w/ practice problems (25 min)
Warm-Up:
1. Place your test corrections in the blue folder
2. Solve for y: x – 2y = 5
HW#1: Cartesian Coordinate System and HW#2: Graphing Linear equations

2. Cartesian Coordinate System
Infinity HS
Ms. Sophia Papaefthimiou

3. Objectives To remember what a the Cartesian coordinate system is
To locate points in the coordinate system
To plot points in the coordinate system

4. Brain Pop Video

5. A Coordinate System The horizontal line is known as the _____.
The vertical line is known as the ______.
The point at which the axes meet or intersect is known as the _____.
A coordinate system has ___ quadrants.
Abscissa
Ordinate
Origin 4

6. Coordinate Plane QUAD II QUAD I QUAD III QUAD IV y-axis
Parts of a plane
x-axis
y-axis
Origin
Quadrants I-IV
QUAD II
QUAD I
Origin ( 0 , 0 )
x-axis
QUAD III
QUAD IV

7. Plotting Points Plot these 4 points: A (3, -4) B (5, 6.5) C (-4, 5)
1. Remember when plotting points you always start at the origin.
2. Next you go left (if x-coordinate is negative) or right (if x-coordinate is positive.
3. Then you go up (if y-coordinate is positive) or down (if y-coordinate is negative) B C D A
Plot these 4 points:
A (3, -4)
B (5, 6.5)
C (-4, 5)
D (-7, 0)

8. Locating Points
RULE: Any point P is represented by an ordered pair of numbers written in the form (x, y)
The x-value is always first and the y-value is always second

9. Graphing linear equations using a table of values
Infinity HS
Ms. Sophia Papaefthimiou

10. Graphing linear equations
To graph a linear equation you can use:
1.) Table of values (today’s lesson)
2.) Intercepts (next project)
3.) Slope intercept form (y = mx + b) (next project)

11. What is a Linear Equation?y x
Linear
A linear equation is an equation whose graph is a LINE.
Not Linear

12. What is a Linear Equation?y x
The equations we will be graphing have two variables, x and y.
For example,
A solution to the equation is any ordered pair (x , y) that makes the equation true.
The ordered pair (3 , 2) is a solution since,
If we were to plot all these ordered pairs on a graph, we would be graphing a line.

13. Ex 1: Graph y = 3x – 2 using a Table of Values
First Step: Solve for y (write y as a function of x)
Second Step: Make a Table of Values x
3x – 2 y
(x, y)

14. The x - values are picked by YOU!
Table of Values x
3x – 2 y
(x, y) –2 –1 1 2
The x - values are picked by YOU!

15. Table of Values x
3x – 2 y
(x, y) –2
3(–2) – 2 -8
(-2, -8) –1 1 2

16. Table of Values x 3x – 2 y (x, y) –2 3(–2) – 2 -8 (-2, -8) –1
3(–1) – 2 -5
(-1, -5)
3(0) – 2 -2
(0, -2) 1
3(1) – 2
(1, 1) 2
3(2) – 2 4
(2, 4)

17. y = 3x – 2 y x

18. Ex 2: Graph x – 2y = 5
First Step: Solve for y (write y as a function of x)
x – 2y = 5
–2y = -x + 5

19. Second Step: Make a Table of Valuesy x x y
(x, y) -2
-3.5
(-2, -3.5) -1 -3
(-1, -3)
-2.5
(0, -2.5) 1
(1, -2) 2
-1.5
(2, -1.5)

20. Graphing Horizontal & Vertical Linesy x
When you are asked to graph a line, and there is only ONE variable in the equation, the line will either be vertical or horizontal. For example …
Graph x = 3
y = –2
Since there are no y–values in this equation, x is always 3 and y can be any other real number.
Graph y = –2
Since there are no x–values in this equation, y is always –2 and x can be any other real number.
x = 3