SWBAT…solve multi-step equations

Agenda 1. WU / Announcements(5 min)2. Announcements (5 min)3. Binder organization (10 min)4. Quiz (15 min)

Warm-Up1. Write the homework in your

planners for the week

HW: Review “PPT1: Cartesian Coordinate System and Linear Equations”

Monday, 10/25/10

Announcements

MSquared Program at Phillips Academy 5 week summer program (June 28 – Aug 3) in Andover,

Massachusetts The (MS)2 program offers three sections of mathematics

for first-year students.  Last summer, sections A and B studied algebra; section C studied pre-calculus.  The topics covered in algebra included: solving linear equations; problem-solving strategies; graphing linear equations; matrix operations; functions and transformations; recursion; probability and statistics. 

The (MS)2 biology course features an intensive examination of topics that are frequently left out of conventional high school biology courses due to lack of time and shortage of laboratory space.

APPLY!!!!! (Pre-application due Dec 20 – go online to download the pre-application)

Announcements (cont’d)

Volunteers interested in Digital Media GroupCommitment: 2 days/week, 2 hours each day

Volunteers interested in Mural LeadersCommitment: 3 days/week, 2 hours each day

Binder Organization (10 min) Use the next 10 minutes to organize your binder I am going to collect and grade your binders later

this week If you are missing any of the sheets, look in the

folders on the front wall If the sheet is not on the wall, write your name and

what you need and hand it to me Using the binder evaluation sheet, grade

yourselves on your binder (top half of the sheet) Fill out the “grades/comments” boxes Give yourself an “overall grade”

SWBAT… graph linear equations using a table of values

Agenda 1. WU (5 min)2. Notes on linear equations w/ practice problems

(30 min)

Warm-Up: Solve for y:3x – 8y = 12

HW#1: Linear Equations

Tuesday, 10/26/10

SWBAT… graph linear equations using a table of values

Agenda 1. WU (10 min)2. Notes on linear equations w/ practice problems (30 min)

Warm-Up 1. On one of the squares, make a coordinate

system plane labeling the x-and y-axis. Label the below points. Glue this in your note book.

A (3, -4) B (5, 6.5) C (-4, 5) D (7, 0) 2. Label the origin3. Label Quadrant I, II, III, IV

HW#1: Linear Equations

Wednesday, 10/27/10

Quiz corrections can be done for ½ points: Due tomorrow

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

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.

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 4 points:A (3, -4)B (5, 6.5)C (-4, 5)D (-7, 0)

A

BC

D

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

Graphing Linear Equations

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 week)

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

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

- + =

Directions: Graph y = 3x – 2 using a Table of Values

x 3x – 2 y (x, y)

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)

The x - values are picked by YOU!

Complete the table by inputting the x - values and calculating the corresponding y - values.

Graphing a Linear Equationy

x

How do we graph linear equations?

Let’s try this one: y = 3x – 2

Make a Table of values

Input (x) Output (y)

–2

–1

0

1

2

y = 3(–2) – 2 = –8

y = 3(–1) – 2 = –5

y = 3(0) – 2 = –2

y = 3(2) – 2 = 4

y = 3(1) – 2 = 1

–8

–5

–2

1

4

y = 3x - 2

Graphing a Linear Equation

Graph x – 2y = 5

First Step:

Write y as a function of x

x – 2y = 5

–2y = 5 – x

5 12 2

y x

Graphing a Linear Equation (cont’d)y

x

Second Step:

Make a Table of Values

x y

–2

–1

0

1

72

52

–3

5 12 2

y x

–2

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