Math Education: Solving and Graphing Linear Equations
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Transcript of Math Education: Solving and Graphing Linear Equations
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Math Education:Solving and Graphing Linear Equations
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HOME
Home InformationMovieReview
PracticeQuizReferences
Info
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Movie
QUIZ
Practice
Review
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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
have!HOME
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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
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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
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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
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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
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CORRECT
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WRONG
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Question #5
1.2x – 6 > 2
A.x > 4
B.x > 2HOME
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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
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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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