TAGALOG: Graphing Linear Inequalities in 2 Variables #TeacherA #MathinTagalog

00:15:38
https://www.youtube.com/watch?v=ZxST81OojWA

Summary

TLDRThe lesson focuses on how to graph linear inequalities with two variables, using examples to demonstrate the process. The instructor begins by explaining the initial step of converting the inequality into an equation by replacing the inequality sign with an equals sign. In example one, the video walks through finding x- and y-intercepts by setting y and x to zero, respectively, to solve the equation. After obtaining the intercepts, the points are plotted on a coordinate plane, and a decision is made whether to draw a solid line or broken line based on the inequality sign. It uses test points, typically the origin, to determine which side of the line represents the solution to the inequality. The second example works through rearranging the equation into slope-intercept form, identifying points, and finally discussing shading the correct region according to the inequality. The video concludes with encouraging viewers to like and share the content for more lessons.

Takeaways

  • 📉 Graph inequalities by converting them to equations.
  • 🧮 Find x-intercept by setting y = 0.
  • 🔄 Determine y-intercept by setting x = 0.
  • ✂ Use a broken line for 'less than' or 'greater than' inequalities.
  • 📍 Plot intercept points on the coordinate plane.
  • 🟩 Shade the solution side determined by the test point.
  • 🔬 Test point (0,0) often used to check solutions.
  • 📏 Slope-intercept form is y = mx + b.
  • 🔽 Negative slope indicates a downward trend from left to right.
  • 🎗 Remember inequality signs dictate the line style.
  • 🖍 Connect points for the boundary line.
  • 📈 Verify shaded area aligns with inequality.

Timeline

  • 00:00:00 - 00:05:00

    The teacher starts by introducing the lesson on graphing linear inequalities in two variables. The first example provided is the inequality 2x + 4y > 8. To graph this, the inequality must be converted into an equation by changing 'greater than' to 'equal to', resulting in 2x + 4y = 8. The intercepts methods are used: setting y to zero to find the x-intercept (x=4), and setting x to zero to find the y-intercept (y=2). These points, (4,0) and (0,2), are plotted on a coordinate plane. Since the original inequality was 'greater than', the line connecting them is broken, indicating that points on the line aren't included in the solution. The solution area is determined by testing a point, typically the origin, in the inequality to see if it holds true or false.

  • 00:05:00 - 00:10:00

    Following the determination of the graph line type as broken due to the 'greater than' symbol, a test point is used to identify the solution area for the inequality 2x + 4y > 8. The origin (0,0) is plugged into the inequality; however, it results in zero greater than eight, which is false. Thus, the region not including the origin is shaded as the solution area to the inequality. Moving on to example two, the inequality 4x + 3y ≤ -2 is introduced. It is initially converted into the equation form 4x + 3y = -12 to use the slope-intercept method. The equation is rewritten in slope-intercept form where y = (-4/3)x - 4, identifying the slope as -4/3 and y-intercept at -4.

  • 00:10:00 - 00:15:38

    The teacher explains plotting the line using the slope of -4/3 and the y-intercept of -4. The slope indicates the line decreases, starting at the y-intercept and moving down four units and right three units, drawing the second point, forming a line. Since the original inequality has a 'less than or equal to' sign, the line is solid. The solution space is checked using the origin again, as 0 < -12 is false. Therefore, the other side of the line represents the solution set. The graph for 4x + 3y ≤ -2 is completed by shading the appropriate region. The teacher encourages viewers to like, share, and subscribe, concluding the lesson.

Mind Map

Video Q&A

  • What is the first step in graphing a linear inequality?

    First, replace the inequality sign with an equals sign to find the line of equality.

  • How do you determine the x-intercept of a linear equation?

    Set y to zero and solve for x in the equation.

  • How do you determine the y-intercept of a linear equation?

    Set x to zero and solve for y in the equation.

  • When should a broken line be used when graphing inequalities?

    A broken line is used when the inequality is greater than or less than, not equal to.

  • What test point is commonly used to determine the solution side of an inequality?

    The origin (0,0) is commonly used as a test point.

  • What does it mean if the test point satisfies the inequality?

    If the test point satisfies the inequality, the solution set is on the side of the test point.

  • How is slope-intercept form represented?

    Slope-intercept form is represented by y = mx + b.

  • What does the 'm' in the slope-intercept form stand for?

    The 'm' represents the slope of the line.

  • What does it mean if the inequality is false at the test point?

    If false, the solution set is on the opposite side from the test point.

  • What are the steps in plotting the second point when given a slope-intercept form?

    Start from the y-intercept and use slope to find the next point by moving up or down and left or right.

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Subtitles
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  • 00:00:16
    good morning guys teacher a here and
  • 00:00:18
    welcome to gur Pino sa America so for
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    today lesson I graphing linear
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    inequalities into variables so simul
  • 00:00:30
    let's have example number
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    one so number one given I 2x + 4 Y is
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    greater than 8
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    so linear inequality so
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    actually
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    inquality linear equation
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    so intercept form
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    form y
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    mx
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    or x and y intercept so example number
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    one gam x and y intercept so first
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    step given wherein instead greater
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    than
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    equs
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    equation so we have 2X + 4 Y is equal to
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    8 so
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    since x and y intercept
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    next X
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    intercept x
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    intercept value y should be
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    zero y
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    Z value X
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    so so we have
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    2X + 4 and then instead now Y is
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    substitute value which is
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    zero then equals
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    8 so since 4 * 0 is
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    0 cancel out so is
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    2x is equal to 8 solving for
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    X divide both sides of the equation by
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    two so that two will be cancelled out X
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    is equal to 8 / 2 is 4 so therefore if Y
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    is z x is four so
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    ordered 4 so first point x AIS next
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    second point which
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    is y Y intercept so Y
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    intercept X as zero so again given 2x I
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    sorry 2
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    x x
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    Zer + 4
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    y = 8 so 2 * 0 is zero so cancel
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    out so 4 y = 8 so solving for y paraa
  • 00:03:34
    four divide both sides by
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    four 4 / 4 I 1 * y i y so cancel
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    out y isal to 8 / 4 I 2 so therefore if
  • 00:03:51
    x is zero Y is 2 so you second ordered
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    pair I
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    02 so
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    Second
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    Step x intercept by setting y to
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    zero Y intercept by setting X to Zero so
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    next step third
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    step
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    points caran coordinate plane so
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    40 soas x
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    AIS so this is our first
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    point and then second point I
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    02 so NASA y
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    AIS and then after that it
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    connect points hopefully straight
  • 00:04:42
    there so
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    therefore now this is for equation since
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    given I
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    inequality greater than greater than or
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    equal to equal sign so that means
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    instead straight line broken
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    line
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    ER broken L
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    there broken line
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    again equal sign inequality symbol
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    greater
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    than
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    okay not
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    yet soltion given
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    inquality
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    soltion
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    numers
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    inity so
  • 00:05:44
    usually test Point origin which is 0 so
  • 00:05:52
    origin so we have here in test
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    point I zer
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    ug xue Z Yue zero given inequality
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    now statement I true
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    then which means numbers
  • 00:06:25
    side
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    solution ordered pairs side solution
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    given inequality now false that
  • 00:06:36
    means solution so P so given so we have
  • 00:06:42
    2X + 4
  • 00:06:45
    Y is greater than
  • 00:06:48
    8 so plug in Z given so 2 *
  • 00:06:56
    0 + 4 * * 0 is greater than 8 so 2 * 0
  • 00:07:04
    is 0 4 + 0 is zero add them together
  • 00:07:09
    still the answer is
  • 00:07:11
    zero
  • 00:07:13
    so0 is greater than eight so true or
  • 00:07:18
    false of course this is
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    false eight zero so since false sh that
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    means solution inequality
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    i
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    n so is
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    shade
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    line
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    soltion inequality
  • 00:07:51
    okay let's have example number
  • 00:07:56
    two okay example number two
  • 00:08:01
    and given I 4x + 3 Y is less than or
  • 00:08:06
    equal
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    to2 so again First Step
  • 00:08:13
    iite given we in instead greater than or
  • 00:08:18
    equal
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    to
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    equals as an equation so
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    4x + 3
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    Y is less than I sorry
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    equals is equal
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    to12 so this time method I slope
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    intercept form which is
  • 00:08:45
    y y =
  • 00:08:49
    mx + b so G
  • 00:08:58
    Ang
  • 00:09:00
    Y
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    intercept plot or given inequality so 4x
  • 00:09:06
    + 3 y =
  • 00:09:09
    -12 transform slope intercept form so 3
  • 00:09:13
    y left side so we have 3 y equals based
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    slope intercept form after equal sign my
  • 00:09:22
    X so
  • 00:09:25
    4X right side equation POS 4X
  • 00:09:32
    4X and then plus b constant this is
  • 00:09:37
    -12 Asus 12 there
  • 00:09:43
    now
  • 00:09:47
    y terms equation
  • 00:09:51
    by so that cancel out 3 y
  • 00:09:57
    equal -4 divided 3 divide so we have -4
  • 00:10:03
    over
  • 00:10:05
    3x and then -12 / 3 p that's
  • 00:10:11
    -4
  • 00:10:13
    so into slope intercept form that's the
  • 00:10:16
    first step the Second Step next step is
  • 00:10:21
    identify
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    SL so M SL
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    X which is -4 over 3 please take note of
  • 00:10:36
    the sign so since negative that
  • 00:10:47
    means and then
  • 00:10:52
    B constant term that's
  • 00:10:56
    -4 Okay so
  • 00:11:02
    m b so
  • 00:11:07
    therefore let's start with our B which
  • 00:11:09
    is Y
  • 00:11:13
    intercept
  • 00:11:15
    yis
  • 00:11:17
    so
  • 00:11:19
    there next step second Point by using
  • 00:11:23
    our M so
  • 00:11:27
    four either going up or going
  • 00:11:31
    down and then you three it's either to
  • 00:11:35
    the right or to the
  • 00:11:37
    [Music]
  • 00:11:41
    left decreasing
  • 00:11:44
    trab from left to right so from
  • 00:11:48
    here
  • 00:11:52
    four four units numerator so from here 1
  • 00:11:57
    2 3 4 so
  • 00:12:00
    St origin and then three units sideways
  • 00:12:05
    so
  • 00:12:14
    since so a negative and a positive
  • 00:12:17
    negative so from here 1 2 3
  • 00:12:22
    so second
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    point
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    or unit from here 1 2 3 4 and then three
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    units to the right 1 2
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    [Music]
  • 00:12:51
    3 form line now tanong what kind of line
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    broken line ba check original given I my
  • 00:13:02
    equal sign so therefore broken
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    line so
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    there
  • 00:13:13
    so
  • 00:13:17
    [Music]
  • 00:13:18
    graph not
  • 00:13:22
    yet Solutions inequality by using our
  • 00:13:27
    test point now Z Z so actually
  • 00:13:34
    numers it's just
  • 00:13:39
    that
  • 00:13:46
    friend
  • 00:13:51
    inity so test
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    point I 0
  • 00:14:00
    0 so inquality 4x + 3 Y is less than or
  • 00:14:09
    equal to
  • 00:14:12
    -2 x y vales n z so 4 * 0 + 3 * 0 is
  • 00:14:21
    less than or equal to
  • 00:14:24
    -12 so 4 * 0 0 3 * 0 0 0 + 0 that is
  • 00:14:29
    equal to H
  • 00:14:31
    zero and
  • 00:14:33
    then is less than or equal to
  • 00:14:36
    -12 now true or false
  • 00:14:40
    statement
  • 00:14:43
    Z or equals a -12 of course not so F to
  • 00:14:50
    fals
  • 00:14:52
    so
  • 00:14:54
    solution
  • 00:14:57
    side so
  • 00:15:00
    0
  • 00:15:05
    false
  • 00:15:08
    babaan so shade
  • 00:15:13
    n so
  • 00:15:16
    therefore graph so graph 4x + 3 Y is
  • 00:15:21
    less than or equal
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    to2 kindly give me a like share
  • 00:15:31
    YouTube video so that's it for today see
  • 00:15:35
    you on my next video
  • 00:15:37
    by
Tags
  • graphing
  • linear inequalities
  • coordinate plane
  • intercepts
  • inequality solutions
  • slope-intercept form
  • test points
  • math tutorial
  • broken line
  • equations