2nd Quarter Math 8

2nd Quarter Math 8

by Patricia Diomampo

​Aim

• Illustrate linear equation in two variables

• ​construct a table of values for x and y given a linear equation

• determine the solutions ​of linear equations in two variables

​10/25/21

​Review:

​Determine whether the given equation is linear in two variables or not

​1. x+y=4

​2. 2x=4y-2

​3. 5x-3=12

​4. 12=2x +3y

​5. x²-3y=-5

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​Action

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​Analysis:

​From the exercises, can you give a generalization about linear equations?

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​Discussion:

​https://www.youtube.com/watch?v=oZYgb7hy2Pk

​refer to shared screen

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​Content book page 45-46

​10/26/21

Multiple Choice

Tell if the given ordered pair is a solution to the equation or not

(2, 3)       x+4y=12

Multiple Choice

Tell if the given ordered pair is a solution to the equation or not

x=4 y= 3, 2x+3y= 17

Multiple Choice

Tell if the given ordered pair is a solution to the equation or not

x=-2 y= 5, -3x-4y= -14

Multiple Choice

Tell if the given ordered pair is a solution to the equation or not

(-5, -2), -5x+2y=-21

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Answer page 23 of your workbook B6 S2 (1-3) 10mins.

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​Upload your answer in the school app. no submission means no seatwork

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Quiz on the next day about Linear Equations

​Using your boards, draw a linear graph for each given equation

​1. 2x+y=4

​2. x-7y=4

​3. 4x-y=20

​4. 3x-2y=6

​5. 6y-4x=12

​6. x=-8

​7. y=9

Open Ended

What have you learned today?

Poll

Rate today's lesson

Day 2​

Aim

• I will be able to:​

• Illustrate the slope of a line

• ​Find the slope of the line given two points

​Action

​Describe the following images below

Analysis​

​How do you describe these images?

​What is common to them? Define slope.

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​Slope m refers to the steepness of a line.

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​Find the slope of line using the given information.

1.       Rise=3   Run= 5

2.       The vertical change is 7 and horizontal change is 5

3.       The lines rises 3 units as it moves 2 units to the left

​Answers

​1. 3/5

​2. 7/5

​3. 3/-2

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​Discussion

​https://www.youtube.com/watch?v=xO5HK_fF4tk

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​refer to shared screen

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​Generalization/ Summary:

​What is slope? What letter represents the slope?

​What is the formula in getting the slope?

​Describe the behavior of the graph depending on the slope.

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​answer page 26 of workbook B7 S1

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​​Upload your answer in the school app. no submission means no seatwork

​

​

Open Ended

What have you learned today?

Poll

Rate today's lesson

​Aim

​Find the slope of a line given an equation and graph

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​Action

​Analysis

How did you find the slope from the previous activity?

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​What if the given equation is in standard form? How are you going to find the slope?

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​Re-write the following into slope-intercept form or standard form

​1.       y= 2x-5

2.       y=-3x+7

3.       2x-y=5

4. 7x-3y-10=0

​Examples:

​Find the slope of the line given the following:

 

1.        3x + 2y = 8

2.        4x + 5y = 12

3.        (1,5) and (6,-2)

4.        (7,3) and (-1,-5)

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Video Tutorial:

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​https://www.youtube.com/watch?v=kFUid4F2Jwg

​Video Tutorial: https://www.youtube.com/watch?v=pvLT114JuQw

​Application

​Workbook

​Aim:

​to determine the x and y intercept given: a) graph b.) intercept-intercept form c.) standard form

Action:​

What is the x and y intercept of the line?

​Analysis

​What is x-intercept?

​What is y-intercept?

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​How are we going to get x or y-intercept if the given is graph?

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​How about if the given is an equation?

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​Discussion

​Refer to shared screen

​Generalization:

​Generalization

​To get the x intercept and y intercept if the given is in standard form:

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• ​set x to zero, then solve for y. That is the y-intercept

• ​set y to zero, then solve for x. That is the x-intercept.

​Application:

content book practice questions page 56-57

​Aim

​Graphs a linear equation given a) any two points; b) the x and y intercepts; c) the slope and a point on the line

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​Describes the graph of a linear equation in terms of its intercepts and slope

​Aim

​Finds the equation of a line given a) two points; b) the slope and a point c) the slope and its intercepts

​Aim

​Solves problems involving linear equations in two variables

​ESLR: Through solving Systems of Linear Equations, Faithians will be patient in analyzing and solving problems through appropriate and accurate decision making by asking for God’s wisdom.

Bible Verse: James 1:15

“If any of you lacks wisdom, let him ask God, who gives generously to all without reproach, and it will be given to him.”

Principle:

Faithians are dependent of God's wisdom to be good problem solvers.

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​Real Life Application:

As a cashier of a 24-hour convenience store, Fanny ​is paid Php 60 per hour plus an additional Php 500 per week since she's working in the evening shift. If she's working 5 hours per day, how much would she be paid in a 4-week duty?

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​How are you going to solve for this problem?

​* We can use different ways to solve this problem.

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*We can just multiply the number of hours she's working in a week, then multiply it again to her rate, add 500 then, multiply it by 4.

​* We can also solve this through the use of the given units of measures as our guide. We can convert the units and then add 500 at the end to solve the problem.

​* We can also use equations to solve this problem.

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​Every problems that we encounter has multiple ways of how to solve it.

​Seeking His way by reading His words is not an option. It is the only way for us to get through with whatever we are facing.

​Aim

​I will be able to:

​

Solve a system of linear equations in two variables by graphing

​Keywords we will use:

​Coincident: Two lines that lie on top of one another

​Consistent: system with either unique or infinite solutions

​Inconsistent: systems with no solution; the lines of this graph will not intersect at any point.

​

​Action:

​Review:

​How do we get the x and y intercepts of the given linear equation in standard form?

​

Open Ended

How do we get the x and y intercepts of the given linear equation in standard form?

Graph the x and y-intercepts

​Group Activity:

A. x+y =4; 3y=6 B. 3x+y=3; 6x+2y=12 C. -x+2y=3; 4x+y=24 D. 6x-4y=12; -3x+2y=-6

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​Each group should draw the graph of 1 system of equations on their boards (you may use jamboard). Share your work when done. Note what pair of lines is represented by each system of equations. Identify the point of intersection if the two lines are intersecting to find its solution.

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Team A: Giba, Dela Paz JM, Dela Paz JJ, Kim A, Gavino, Arro, Gonzalez

Team B: Guiruela, Basa, Acuna, Donasco, Dalere, Rogelio

Team C: Napay, San Diego, Estipona, Casinsinan, Valencia, Kim E, Pacheco

Team D: Castaneda, Tagal, Jose, Ablana, Bonsol, Gigante

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​10 mins.

​Analysis

What pair of lines ​was represented by each system of linear equations?

​

​*Presentation of each group's work

​A. x+y=4; 3y=6

​B. 3x+y=3; 6x+2y=12

​C. -x+2y=3; 4x+y=24

​D. 6x-4y=12; -3x+2y=-6

​Generalized Discussion:

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​What are the steps did you do to solve the systems of linear equation with 2 variables graphically?

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Generalized Discussion:​

Solving a System of Linear Equations with 2 Variables Graphically

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​Step 1: Plot the graph of the first equation

​Step 2: Plot the graph of the second equation

​Step 3: Identify the point of intersection

​​Generalized Discussion:​

​What does the intersecting lines in a graph represents?

Generalized Discussion:

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​How can we solve a systems of linear equations graphically?

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Fill in the Blanks

Multiple Choice

A/An _______ system has solutions.

• consistent

• inconsistent

​HOTS

Find the ratio ​of the coefficients of x, y, and the constants in both the equations of each type of system.

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​Application

​Answer your workbook Q2 B8 S1 on page 2

Open Ended

What have you learned today?

Poll

Rate today's lesson

​Aim

​Categorizes when a given system of linear equations in two variables has graphs that are parallel, intersecting and coinciding.