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

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Presentation Transcript

Target Audience

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High School Math Students (grades 9-10)

Math Teachers

College Students

Teacher Assistants

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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Information

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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.

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 have!

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What is a linear equation??

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

variables by using any of the

relational symbols such as <,

>, ≤ or ≥ . It also divides a

plane 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 is

dotted, 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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Physics

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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.

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Economics

Economics

Total 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

Engineering

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

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Chemistry

Chemistry

The 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

Statistics

In 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 ^ 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

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Examples of Linear Equations

- 2x = 4
- x + 2 = y
- 2x + 4y = 6

- Can have one variable
- Can have 2 variables
- Can be an inequality

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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

4x – 2y > 12

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

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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

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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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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

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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

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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!!!

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CORRECT

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WRONG

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CORRECT

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WRONG

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WRONG

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WRONG

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WRONG

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CORRECT

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WRONG

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CORRECT

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WRONG

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WRONG

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WRONG

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