2 3 11
Download
1 / 30

2-3-11 - PowerPoint PPT Presentation


  • 103 Views
  • Uploaded on

2-3-11. Please have hw out to correct. Equations with Two Variables. Lesson 8-2 p.391. Equations with Two Variables. In the other chapters, we learned how to solve equations like this: 5x + 3 = 2x +9 In this type of equation, there was only one kind of variable—”x”.

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 ' 2-3-11' - lucius-weaver


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
2 3 11
2-3-11

  • Please have hw out to correct.



Equations with two variables1
Equations with Two Variables

  • In the other chapters, we learned how to solve equations like this:

  • 5x + 3 = 2x +9

  • In this type of equation, there was only one kind of variable—”x”.

  • Now we will learn how to solve variables like: y = 2x + 3


Equations with two variables2
Equations with Two Variables

y = 2x + 3

  • What do you notice about this equation?


Equations with two variables3
Equations with Two Variables

  • y = 2x + 3

  • What do you notice about this equation? Yes there are two kinds of variables—an x and a y.

  • We will find in this chapter that the solution to this type of equation is an ordered pair and if we graph the ordered pairs of the equation, we get a straight line when the points are connected.


Equations with two variables4
Equations with Two Variables

  • We will also find that an equation like y = 2x + 3 can have many solutions, not just one, but it is the graph of the solutions that will be our answer.

  • Let’s start with one way to solve this type of problem. . .a t-table or t-chart


Equations with two variables5
Equations with Two Variables

  • y = 2x + 3

  • One strategy is to make a table of values or a t-table.

  • It looks like this:

    X Y


Equations with two variables6
Equations with Two Variables

  • y = 2x + 3

  • We begin by choosing any value we want for x. This may seem odd to you, but the reason will become apparent later.

  • I like to choose one positive number, one negative number and the number zero.


Equations with two variables7
Equations with Two Variables

  • y = 2x + 3 Let’s choose 1, 0 and -2

    x y

    1 Place the x values in

    0 the chart. This reminds

    -2 us which numbers to

    substitute for x.


Equations with two variables8
Equations with Two Variables

  • y = 2x + 3 Then we substitute each

    value one at a time and

    x y solve for “y”

    1 52(1) + 3 = 5

    0

    -2


Equations with two variables9
Equations with Two Variables

  • y = 2x + 3 Then we substitute each

    value one at a time and

    x y solve for “y”

    1 52(1) + 3 = 5

    0 3 2(0) + 3 = 3

    -2


Equations with two variables10
Equations with Two Variables

  • y = 2x + 3 Then we substitute each

    value one at a time and

    x y solve for “y”

    1 52(1) + 3 = 5

    0 3 2(0) + 3 = 3

    -2 -1 2(-2) + 3 = -1


Equations with two variables11
Equations with Two Variables

  • The information in the t-table is a series of ordered pairs that when graphed on the coordinate plane, will result in a straight line like this


Equations with two variables12
Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)


Equations with two variables13
Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)


Equations with two variables14
Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)

Then plot point (0,3)


Equations with two variables15
Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)

Then plot point (0,3)


Equations with two variables16
Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)

Then plot point (0,3)

Then plot point (-2,-1)


Equations with two variables17
Equations with Two Variables

x y

1 5

0 3

-2 -1

First, plot point (1,5)

Then plot point (0,3)

Then plot point (-2,-1)

Finally draw a line that connects and goes through the points.


Equations with two variables18
Equations with Two Variables

This is the graph of the equation:

y = 2x + 3

We will find that each equation has its own unique graph.


Try this
Try This

  • Make a t-table for the equation

    y = 3x -2 using the following values

    for x

    x y

    3

    0

    -1


Try this1
Try This

  • Make a t-table for the equation

    y = 3x -2 using the following values

    for x

    x y

    3 73(3) – 2 = 7

    0

    -1


Try this2
Try This

  • Make a t-table for the equation

    y = 3x -2 using the following values

    for x

    x y

    3 73(3) – 2 = 7

    0 -2 3(0) – 2 = -2

    -1


Try this3
Try This

  • Make a t-table for the equation

    y = 3x -2 using the following values

    for x

    x y

    3 73(3) – 2 = 7

    0 -2 3(0) – 2 = -2

    -1 -5 3(-1) – 2 = -5


Try this4
Try This

x y

3 7

0 -2

-1 -5

Now graph the

Ordered pairs


Try this5
Try This

x y

3 7

0 -2

-1 -5


One more thing
One more Thing

  • Sometimes, an equation will be given as well as a sample ordered pair, and you will be asked “Is this a solution to the equation?”

  • For example, is (4,3) a solution to this equation: y = -2x + 2

  • Substitute the ordered pair in the solution: 3 = -2(4) + 2

    In this case 3 = -8 + 2 or

    3 = -6 is not true, so no it is not a solution.


Try this6
Try This

  • Is (3,0) a solution to y = 2x – 6

  • 0 = 6 – 6

  • 0=0

  • Is (-2,5) a solution to y = -3x + 1

  • 5 = 7


Try this7
Try This

  • Is (3,0) a solution to y = 2x – 6 yes

  • Is (-2,5) a solution to y = -3x + 1 no


2 3 11 agenda
2-3-11 Agenda

PA#13:

Pp.394-395

#12-18 even, 20-30 even


ad