Math Education:Solving and Graphing Linear Equations

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Info

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Movie

QUIZ

Practice

Review

High School Math Students (grades 9-10)

Math Teachers College Students Teacher Assistants

Target Audience

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Math Courses Reference for

homework Computer labs Review In Class Lesson

Learning Environment

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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.

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

Information

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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?!?

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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

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What is a linear equation??

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

Well, lets find out!!!

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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

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

expressions?

A Linear Inequality involves a

linear expression in twovariables by using any of

therelational symbols such as

<,>, ≤ or ≥ . It also divides aplane into two parts.

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Linear Inequalities...

If the boundary line is solid, then the linear inequality must be

either ≥ or ≤.

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Linear Inequalities...

If the boundary line isdotted, then the linear

inequality must be either >or <.

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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.

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PhysicsA 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.

Physics

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Temperature

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

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Economics

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

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Engineering

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

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Chemistry

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

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Statistics

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

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Examples of Non-Linear Expression

x ^ 22xy + 42x / yx ^ 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

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Examples of Linear Equations

2x = 4x + 2 = y2x + 4y = 6

Can have one variable

Can have 2 variables

Can be an inequality

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Movie on how to solve a

linear equation

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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!

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Review Question

2x + 2 = 10

1. 2x +2 -2 = 10 -2

2. 2x /2 = 8 /23. X = 4

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Review Question

 4x - 4y = 8

1. 4x – 4y +4y = 8 +4y

2. 4x -8 = 4y -83. 4x /4 – 8 /4 = 4y /4

4. x – 2 = y

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Review Question

4x – 2y > 12

1. 4x – 2y +2y > 12 +2y

2. 4x -12 > 12 -12 +2y

3. 4x /2 – 12 /2 > 2y /2

4. 2x – 6 > y HOME

Review Question

Graph y = 3x + 1

1. First, graph the y-intercept point on the

y-axis “up 1”2. Then begin graphing

the slope “up 3, over 1” and “down 3 left 1”

3. Finally draw a line through the points

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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!

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Practice…practice…practice…

2x + 3 = 15

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Solution

1. 2x + 3 = 152. 2x + 3 -3 =

15 -33. 2x /2 = 12 /24. x = 6

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Practice…practice…practice…

3x – 2y = 14

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Solution

1. 3x – 2y = 142. 3x – 2y +2y = 14

+2y3. 3x -14 = 14 -14 +2y4. 3x /2 - 14 /2 = 2y /25. y = 3x/2 - 7

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Practice…practice…practice…

2x + 8 > 4

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Solution

1. 2x + 8 > 42. 2x + 8 -8 >

4 -83. 2x /2 > -4 /24. x > -2

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Practice…practice…practice…

Graph: Y = 2x +

4HOME

Solution1. y = 2x + 42. First, plot the point

(0, 4)3. Then, plot the points

“up 2 over 1” and then “down 2 left 1”

4. Finally, complete the grapy by drawing a line through the points

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Practice…practice…practice…

Graph:Y > 2x/3

+ 2HOME

Solution1. First, plot the point

(0, 2) 2. Then, plot the points

“down 2 over 3” and then “up 2 left 3”

3. Next, complete the grapy by drawing a line through the points

4. Finally, since it’s a less than sign, shade underneath the line

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Quiz!!!

You’ll be given 10 questions based off what you’ve

learned from this powerpoint. 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!!!

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Question #11.6x – 12 = -24

A.x = -2

B.x= -6

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CORRECT

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WRONG

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Question #21.5x – 10 = 90

A.x = 16

B.x = 20

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CORRECT

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WRONG

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Question #31.6x – 2y = -10

A.y = 3x + 5

B.y = -3x - 5

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CORRECT

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WRONG

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Question #41.3x + 3y =

12

A.y = 6x - 4

B.y = -x + 4HOME

CORRECT

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WRONG

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Question #5

1.2x – 6 > 2

A.x > 4

B.x > 2HOME

CORRECT

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WRONG

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Question #61.10x – 6y + 3 <

13

A.y < 3x/5 + 5/3

B.y < 5x/3 - 5/3HOME

CORRECT

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WRONG

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Question #71. y = 2x + 1

A. Graph 1 B. Graph 2

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CORRECT

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WRONG

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Question #81. y = -x + 2

A. Graph 1 B. Graph 2

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CORRECT

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WRONG

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Question #91. y < -x + 1

A. Graph 1 B. Graph 2

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CORRECT

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WRONG

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Question #101. y < -x/2 + 2

A. Graph 1 B. Graph 2

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CORRECT

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WRONG

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YOU FINISHED!!!!!

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