SWBAT… review the Cartesian Coordinate system & graph linear equations using a table of values

Agenda 1. WU (10 min)2. Review Cartesian Coordinate System (10 min)3. Notes on linear equations (10 min)4. 2 graphing examples (20 min)

Warm-Up:1. Write your HW in your planner for the

week

2. Solve for y: y – 3x = -2 3. Solve for y: x – 2y = 5

One Application Graphing Problem (on graph paper)

Tues, 10/9

We have begun a new unit on Functions:

Students will be able to:

1. Know the Cartesian Coordinate System (HW1)

2. Graph linear functions (equations) using a table of values (HW2)

3. Graph absolute value functions (HW3)

4. Graph piecewise functions (HW4)

5. Write algebraic equations given various forms of data (table, graph, words) (HW5)

6. Evaluate a function and write as an ordered pair (HW6)

7. List the domain and range of a function (HW7)

8. Determine if a relation is a function using the vertical line test or given a mapping diagram (HW8)

Cell phone project after October break!

Unit test after October break!

Cartesian Coordinate System

Infinity HS

Ms. Sophia Papaefthimiou

Objectives

1. To remember what a the Cartesian coordinate system is

2. To locate points in the coordinate system

3. To plot points in the coordinate system

The Cartesian Coordinate System The horizontal line (x-axis) is known as the ________. The vertical line (y-axis) is known as the _ _____. The point at which the axes meet or intersect is known as the

_____. A coordinate system has ___ quadrants. Any point P is represented by an _ ____ _ of numbers

written in the form (x, y). The __-value is always first and the __-value is always second When a point is plotted on the coordinate system, a _______ x

value indicates a movement to the left. A _______ y value indicates a movement down.

abscissaordinate

origin4

ordered pair

x y

negativenegative

Coordinate Plane

Parts of a plane1. x-axis2. y-axis3. Origin4. Quadrants I-IV

x-axis

y-axis

Origin ( 0 , 0 )

QUAD IQUAD II

QUAD III QUAD IV

Plotting Points

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)

Plot these points:A (3, -4)B (5, 6.5)C (-4, 5)D (-7, 0)E (0, -4)F (0, -1)G (0, π) = (0, 3.14)

A

BC

DF

E

G

Daniela plotted the coordinates of the 2 largest toy shops in the city. The coordinates of Shop A are (2,6). The coordinates of Shop B are in Quadrant II with the same y-coordinate as Shop A. What are the coordinates of Shop B?

A. (2,0)B. (3,6)

C. (4,−6) D. (-5,6)

(2, 6)QUAD II

Graphing linear equations using a table of values

Infinity HS

Ms. Sophia Papaefthimiou

Graphing linear equations

To graph a linear equation you can use:1.) Table of values (today’s lesson)

2.) Intercepts (next unit)

3.) Slope intercept form (y = mx + b) (next unit)

What is a Linear Equation?

A linear equation is an equation whose graph is a LINE.

y

x

Linear

Not Linear

( ) ( )2 3 3 2 12+ =

What is a Linear Equation?

A solution to the equation is any ordered pair (x , y) that makes the equation true.

If we were to plot all these ordered pairs on a graph, we would be graphing a line.

The equations we will be graphing have two variables, x and y.

2 3 12x y+ =

y

x

For example,

The ordered pair (3 , 2) is a solution since,

( ) ( )2 0 3 4 12+ =

( ) ( )2 6 3 0 12+ =

( ) ( )2 3 3 6 12- + =

( ) ( )22 1 3 4 123

- + =

Ex 1: Graph y – 3x = -2 using a Table of Values

x 3x – 2 y (x, y)

Step 1: Solve for y (write y as a function of x)

Step 2: Make a Table of Values

Step 2: Make a Table of Values

The x - values are picked by YOU!

x 3x – 2 y (x, y)

–2

–1

0

1

2

Step 2: Make a Table of Values

x 3x – 2 y (x, y)

–2 3(–2) – 2 -8 (-2, -8)

–1

0

1

2

Step 2: Make a Table of Values

x 3x – 2 y (x, y)

–2 3(–2) – 2 -8 (-2, -8)

–1 3(–1) – 2 -5 (-1, -5)

0 3(0) – 2 -2 (0, -2)

1 3(1) – 2 1 (1, 1)

2 3(2) – 2 4 (2, 4)

y = 3x – 2y

x

Step 3:Plot the ordered pairs

Step 4:Label the line

Ex 2: Graph x – 2y = 5

Step 1: Solve for y (write y as a function of x)

x – 2y = 5

–2y = -x + 5

2

5–x

2

1y

y

x

Step 2: Make a Table of Values

x y (x, y)

-2 -3.5 (-2, -3.5)

-1 -3 (-1, -3)

0 -2.5 (0, -2.5)

1 -2 (1, -2)

2 -1.5 (2, -1.5)

2

5–x

2

1

2

5–(-2)

2

1

2

5–(-1)

2

1

2

5–(0)

2

1

2

5–(1)

2

1

2

5–(2)

2

1

2

5–x

2

1y

Step 3: Plot the ordered pairs

Step 4: Label the line

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

Since there are no y–values in this equation, x is always 3 and y can be any other real number.

x = 3

Graph y = –2

Since there are no x–values in this equation, y is always –2 and x can be any other real number.

y = –2

Application HW Problem – Do on graph paper

A student makes $8 per hour at his part time job. Create a table of values and a graph to represent how much money he would earn if he worked the following hours: 15 hrs, 20 hrs, 22 hrs, 28 hrs.

x (hours worked)

y = 8x y (money earned)

(x, y)