math education solving and graphing linear equations n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Math Education: Solving and Graphing Linear Equations PowerPoint Presentation
Download Presentation
Math Education: Solving and Graphing Linear Equations

Loading in 2 Seconds...

play fullscreen
1 / 72

Math Education: Solving and Graphing Linear Equations - PowerPoint PPT Presentation


  • 93 Views
  • Uploaded on

Math Education: Solving and Graphing Linear Equations. HOME. HOME. Practice. Home Information Movie Review. Practice Quiz References . HOME. Info. QUIZ. Movie. Review. Target Audience. HOME. High School Math Students (grades 9-10) Math Teachers College Students

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Math Education: Solving and Graphing Linear Equations' - nani


Download Now An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2
HOME

Practice

  • Home
  • Information
  • Movie
  • Review
  • Practice
  • Quiz
  • References

HOME

Info

QUIZ

Movie

Review

target audience
Target Audience

HOME

High School Math Students (grades 9-10)

Math Teachers

College Students

Teacher Assistants

learning environment
Learning Environment

HOME

Math Courses

Reference for homework

Computer labs

Review

In Class Lesson

objectives
Objectives

This power point offers a section of information, review, practice, a movie, and a quiz to help teach anyone how, when and why linear expressions and equations are used. I expect the learner be able to score at least a 80% on the quiz after they’ve reviewed this power point.

HOME

information
Information

HOME

This section of the power point will give you the knowledge to be able to solve and understand the uses of different linear expressions.

linear
LINEAR?

The word “linear” pertains to something only having one dimension. It’s a straight line. When a linear equation is correctly graphed it forms a straight line on a graph!

Amazing, right?!?

HOME

some questions you may have in your head as we begin this lesson
Some questions you may have in your head as we begin this lesson….
  • What is a linear equation?
  • What is an inequality and what do they have to do with linear expressions?
  • Why will I ever need to learn this material?

Lets move forward to answer all these questions and any others you might have!

HOME

what is a linear equation
What is a linear equation??

Do any of the equations on the chalk board look like they couldbe linear equations?

Well, lets find out!!!

HOME

a linear equation is
A linear equation is…..

An algebraic equation, such as

y = 2x + 7 or 3x + 2y − z = 4, in which the highest degree term in the variable or variables is of the first degree. The graph of such an equation is a straight line if there are two variables. It is often written in the form of y=mx+b

HOME

what is an inequality and what do they have to do with linear expressions
What is an inequality and what do they have to do with linear expressions?

A Linear Inequality involves a

linear expression in two

variables by using any of the

relational symbols such as <,

>, ≤ or ≥ . It also divides a

plane into two parts.

HOME

linear inequalities
Linear Inequalities...

If the boundary line is solid, then the linear inequality must be either ≥ or ≤.

HOME

linear inequalities1
Linear Inequalities...

If the boundary line is

dotted, then the linear

inequality must be either >

or <.

HOME

let s talk about how such expressions could be important to you
Let’s talk about how such expressions could be important to you…
  • Physics
  • Conversion of Units
  • Economics
  • Engineering
  • Chemistry
  • Statistics

The things listed to the left are all ways people use linear equations in life and can be clicked on to take you to that specific description.

HOME

physics
Physics

HOME

Physics

A simple example from physics is Hooke's law, which states the force of a spring is proportional to the distance it is extended or compressed.

temperature
Temperature

Conversion of Units

Fahrenheit and Celsius are convertible by a linear equation: F - 32 = 9 C / 5.

HOME

economics
Economics

Economics

Total cost is often a function of fixed cost plus variable cost times some variable quantity (or the sum or such products).

HOME

engineering
Engineering

Engineering

The heat transfer through a material is proportional to the thickness of the material.

HOME

chemistry
Chemistry

Chemistry

The gas equation, PV=nRT, when two of the four variables are known, often because they are selected, becomes a linear equation.

HOME

statistics
Statistics

Statistics

In statistics, linear regression is a common model for testing correlation. Assumptions of the model, including linearity, make testing computationally much simpler.

HOME

examples of non linear expression
Examples of Non-Linear Expression
  • x ^ 2
  • 2xy + 4
  • 2x / y
  • x ^ ½
  • No variables can be squared
  • Variables can’t be multiplied together
  • Variables can’t be divided by each other
  • Can not take the square root of variables

HOME

examples of linear equations
Examples of Linear Equations
  • 2x = 4
  • x + 2 = y
  • 2x + 4y = 6
  • Can have one variable
  • Can have 2 variables
  • Can be an inequality

HOME

this is what we know
This is what we know
  • We’ve gone over what a linear equation is.
  • What inequalities are and how they relate to linear expressions.
  • And where these could be used for jobs and everyday life.

Lets go over how to do a few problems!

HOME

review question
Review Question

2x + 2 = 10

  • 2x +2 -2 = 10 -2
  • 2x /2 = 8 /2
  • X = 4

HOME

review question1
Review Question

4x - 4y = 8

  • 4x – 4y +4y = 8 +4y
  • 4x -8 = 4y -8
  • 4x /4 – 8 /4 = 4y /4
  • x – 2 = y

HOME

review question2
Review Question

4x – 2y > 12

  • 4x – 2y +2y > 12 +2y
  • 4x -12 > 12 -12 +2y
  • 4x /2 – 12 /2 > 2y /2
  • 2x – 6 > y

HOME

review question3
Review Question

Graph y = 3x + 1

  • First, graph the y-intercept point on the y-axis “up 1”
  • Then begin graphing the slope “up 3, over 1” and “down 3 left 1”
  • Finally draw a line through the points

HOME

on your own
On your own!

Now that you’ve watched a

movie and have seen some

example problems on

solving a linear equation why

don’t you try a few on your

own!? Just click to the next

slide, then try to solve the

problem on your own. When

ready to view the answer click

the arrow!

HOME

solution
Solution
  • 2x + 3 = 15
  • 2x + 3 -3 = 15 -3
  • 2x /2 = 12 /2
  • x = 6

HOME

solution1
Solution
  • 3x – 2y = 14
  • 3x – 2y +2y = 14 +2y
  • 3x -14 = 14 -14 +2y
  • 3x /2 - 14 /2 = 2y /2
  • y = 3x/2 - 7

HOME

solution2
Solution
  • 2x + 8 > 4
  • 2x + 8 -8 > 4 -8
  • 2x /2 > -4 /2
  • x > -2

HOME

solution3
Solution
  • y = 2x + 4
  • First, plot the point (0, 4)
  • Then, plot the points “up 2 over 1” and then “down 2 left 1”
  • Finally, complete the grapy by drawing a line through the points

HOME

practice practice practice4
Practice…practice…practice…

Graph:

Y > 2x/3 + 2

HOME

solution4
Solution
  • First, plot the point (0, 2)
  • Then, plot the points “down 2 over 3” and then “up 2 left 3”
  • Next, complete the grapy by drawing a line through the points
  • Finally, since it’s a less than sign, shade underneath the line

HOME

slide40
Quiz!!!

You’ll be given 10 questions

based off what you’ve

learned from this power

point. There are two

choices to pick from and

you must correctly answer

each one to move on. Click on whichever one you think is correct to find the answer.

GOOD LUCK!!!

HOME

question 1
Question #1
  • 6x – 12 = -24
  • x = -2
  • x= -6

HOME

wrong
WRONG

HOME

question 2
Question #2
  • 5x – 10 = 90
  • x = 16
  • x = 20

HOME

wrong1
WRONG

HOME

question 3
Question #3
  • 6x – 2y = -10
  • y = 3x + 5
  • y = -3x - 5

HOME

wrong2
WRONG

HOME

question 4
Question #4
  • 3x + 3y = 12
  • y = 6x - 4
  • y = -x + 4

HOME

wrong3
WRONG

HOME

question 5
Question #5
  • 2x – 6 > 2
  • x > 4
  • x > 2

HOME

wrong4
WRONG

HOME

question 6
Question #6
  • 10x – 6y + 3 < 13
  • y < 3x/5 + 5/3
  • y < 5x/3 - 5/3

HOME

wrong5
WRONG

HOME

question 7
Question #7
  • y = 2x + 1
  • Graph 1B. Graph 2

HOME

wrong6
WRONG

HOME

question 8
Question #8
  • y = -x + 2
  • Graph 1 B. Graph 2

HOME

wrong7
WRONG

HOME

question 9
Question #9
  • y < -x + 1
  • Graph 1B. Graph 2

HOME

wrong8
WRONG

HOME

question 10
Question #10
  • y < -x/2 + 2
  • Graph 1B.Graph 2

HOME

wrong9
WRONG

HOME

references
REFERENCES
  • http://t1.gstatic.com/images?q=tbn:ANd9GcT7zLnCmvdbMzFRkeXiYz3X66P86ueVWQ9SiJYRHwSex6liQ26L
  • http://t0.gstatic.com/images?q=tbn:ANd9GcT_MmkrqG6ChnwaFjS9F0a_i-lSfWwaORAeIcw1HaQCGAQAqnbEcQ
  • http://t3.gstatic.com/images?q=tbn:ANd9GcSX9mOHGml3FRziAIWdn_RZM5bVjFvEmALQ1WxDmedydeeLASZldg
  • http://t3.gstatic.com/images?q=tbn:ANd9GcRBB7AWhw2uoS4QmQEgw2_oMVr1I_s-qIg8qLj-wSNEa53zADNX
  • http://teflworldwiki.com/images/0/06/Question-mark.jpg
  • http://t0.gstatic.com/images?q=tbn:ANd9GcSd6wFGPuaVfNM9R_b63eW7vjkGbx4KBfN1pQmzJZzoQdYtdMcD0A
  • http://t1.gstatic.com/images?q=tbn:ANd9GcRPr47slZBPH0TWwq3eUaGephEHaPTVWjz4xc8kMjthLLZFqYV9
  • http://t2.gstatic.com/images?q=tbn:ANd9GcRD72gpga0OJoUaWxDARbN09NQw35sUyG_kNUFhkjZ21PI8b28R7Q
  • http://t2.gstatic.com/images?q=tbn:ANd9GcQ59nU7ra2e0MHpvvTTgw_N3JDDZ0QJFQ_z7Fs7pF-NIYkLfvx1DA
  • http://t1.gstatic.com/images?q=tbn:ANd9GcSx8jHmB-lDtPJdY1XiYqbG2vbwyj3t6AZf48QfKdPZyjuO7JX7
  • http://www.intmath.com/Plane-analytic-geometry/2x-4.gif
  • http://textbooks.cpm.org/glossary/ac/ACglossB/B-8.jpg
  • http://t2.gstatic.com/images?q=tbn:ANd9GcRds-hxpQ6gRhfkEh4A23LZxUgYX0f3v6xojPry5OE3mPje8d1A6w
  • http://t3.gstatic.com/images?q=tbn:ANd9GcQUhwL3RxulJMnQJX7lWiKSULJVcF8S-tGG98FUfMQYOZf-0kiqoQ
  • http://t1.gstatic.com/images?q=tbn:ANd9GcSOsUdTW0K6BbgFcVadIqNr2s1sIXIaTz9IKY_75Nh1zF5_c0sXEA
  • http://t2.gstatic.com/images?q=tbn:ANd9GcSYhKmpbdIZjphflh-BnrSisWXLKSEdiQ1GQHLcMtBWr7wdB6eR8g
  • http://t2.gstatic.com/images?q=tbn:ANd9GcQlLVp7B3Ir6bh3PXI_siSluQt4u9-Fo_7Mj1rDwKBk3aL-0uN1Pg
  • http://t1.gstatic.com/images?q=tbn:ANd9GcS3JGPfQOJ_DOprxmfDtKdIv5gHS0TQIjtvRjMkNpGevPP3pnxoQQ
  • http://t0.gstatic.com/images?q=tbn:ANd9GcRuWzbrN96yuYhnPqLavOJiiVHwTWk7sZW0_kpOSfNl01vDbsRq8A
  • http://t1.gstatic.com/images?q=tbn:ANd9GcTaNz-BP11o3FsqEy0gqdbZhBYOWECbU1w28zemv-F7g3uzhSIyLw
  • http://robertjloomis.com/wp-content/uploads/2010/11/confused-cartoon-face2.jpg
  • http://t2.gstatic.com/images?q=tbn:ANd9GcR4XKrSHU3MqNyqUmLbNZ3jYsrOn7TsK7dfI493SciEzmhh-ixx
  • http://t3.gstatic.com/images?q=tbn:ANd9GcS53U6z569kHnwywKkdcFIZ_TxazHxRqPWMMaYRp1SydHm5Tg2dsA
  • http://t1.gstatic.com/images?q=tbn:ANd9GcT4TTLr_lBw0oj_mANsG_YyWkIRctm_-JhsYmK-bQuK_Vsw4_hn
  • http://ww2.justanswer.com/uploads/abozer/2010-01-18_235240_1.jpg
  • http://cnx.org/content/m22015/latest/C11_S11-6_P17_010.jpg
  • http://www.algebra.com/algebra/lessons/graphing/linear.jpg
  • http://t2.gstatic.com/images?q=tbn:ANd9GcRELCFj1nnaAicr6VQEMu9fqp96rwHUO1NS8OehPg3NjzZL9woV
  • http://t3.gstatic.com/images?q=tbn:ANd9GcR98ymljVuDZ9Q5QDMSWOMhs6aDDS2-ogKn0WFtn7poTHsqVj4hsQ
  • http://t2.gstatic.com/images?q=tbn:ANd9GcQ_s5_iLazVHX7cP8WlYmXOE6h2Ud2dmPuRuEjugCTmVWOjpqcsAQ