Math Education: Solving and Graphing Linear Equations

1 / 72

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

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

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

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

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

### 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

Teacher Assistants

Learning Environment

HOME

Math Courses

Reference for homework

Computer labs

Review

In Class Lesson

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

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?

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

• 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??

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

Well, lets find out!!!

HOME

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?

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...

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

HOME

Linear Inequalities...

If the boundary line is

dotted, then the linear

inequality must be either >

or <.

HOME

• 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

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

Conversion of Units

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

HOME

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

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

HOME

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

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
• 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
• 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
• 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

2x + 2 = 10

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

HOME

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 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 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

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

the arrow!

HOME

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

HOME

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

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

HOME

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…practice…

Graph:

Y > 2x/3 + 2

HOME

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

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

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

GOOD LUCK!!!

HOME

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

HOME

WRONG

HOME

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

HOME

WRONG

HOME

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

HOME

WRONG

HOME

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

HOME

WRONG

HOME

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

HOME

WRONG

HOME

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

HOME

WRONG

HOME

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

HOME

WRONG

HOME

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

HOME

WRONG

HOME

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

HOME

WRONG

HOME

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

HOME

WRONG

HOME

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://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://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