HOMETOWN PUZZLER

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There are four friends who come from different parts of the Philippines. They are Lito, Nelia, Lucy and Mitoy.

Whenever they are asked where their hometowns are, they would show a map and each would say,

Lito: “My hometown falls on the line represented by the equation x = -5.”

Nelia: “My hometown falls on the line represented by the equation y = -11.”

Lucy: “My hometown falls on the line represented by the equation y = 3x + 6.”

Mitoy: “My hometown falls on the line represented by the equation 2x + 5y = 10.”

Your teacher will give you the map. The black dots in that map represent different possible hometowns. Can you find out where their hometowns are?

For you to be able to answer this, you have to learn how to graph linear equations in the coordinate system.

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Express the equation in slope-intercept form and use the slope and the y-intercept to

graph the line.

Determine the slope of the line represented by

the equation and draw a line with

this slope starting from the origin

Plot an ordered pair satisfying the

equation and connect this point with the origin to

create a line.

Make a table of ordered pairs satisfying the

equation and use these to graph the

line.

Graphing linear

equations in the

coordinate system

Which of the methods in the above diagram will lead you to graphing linear equations in the coordinate system? Be ready to explain your choice.

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THINKING ABOUT OUR CHOICESPlot an ordered pair satisfying the equation and connect this point with the origin to create a line.

What is the use of the ordered pair in graphing a line? __________________________________________________________________________

Why does the line need to pass through the origin? __________________________________________________________________________

Express the equation in slope-intercept form and use the slope and the y-intercept

to graph the line. What is the use of the y-intercept in graphing a line? __________________________________________________________________________

What is the use of the slope in graphing a line? __________________________________________________________________________

Determine the slope of the line represented by the equation and draw a line with this slope starting from the origin.What is the use of the slope in graphing a

line? __________________________________________________________________________

Why does the line need to pass through the

origin? __________________________________________________________________________

Make a table of ordered pairs satisfying the equation and use these to graph the line.

How do you make a table of ordered pairs? __________________________________________________________________________

How do you use the ordered pairs to graph the

line? __________________________________________________________________________

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LESSON 1:

To learn about graphing linear equations, click on the website below:

http://www.purplemath.com/modules/graphlin.htm

ACTIVITY 1

Fill in the T-Chart of the following equations with at least three ordered pairs.

2x + y = 6

x = 3

After learning from this website, answer the activity on the right.

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LESSON 2:

To learn more about graphing linear equations, click on the website below:

http://www.math.com/school/subject2/lessons/S2U4L3GL.html

ACTIVITY 2

Carefully analyze the two equations below then answer the following questions.

After learning from this website, answer the activity on the right.

- 2x + 3y = 3

a. How would you express this equation in slope-intercept form? ______________________________

b. What is its y-intercept? _________

c. What is the slope of this line? ____

y = 5

a. How would you express this equation in slope-intercept form? ______________________________

b. What is its y-intercept? _________

c. What is the slope of this line? ____

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GUIDED PRACTICE

ACTIVITY 3

Let us go back to the equations that you have answered in ACTIVITY 1. Using the T-Chart of ordered pairs, graph these two equations on a graphing paper. Draw a separate coordinate system for each equation.

ACTIVITY 4

Let us go back to the equations that you have answered in ACTIVITY 2. Using the y-intercept and slope of the line, graph these two equations on a graphing paper. Draw a separate coordinate system for each equation.

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INDEPENDENT PRACTICE

Now you are ready to graph linear equations on your own!

Click on the website address below and graph the given linear equations on a graphing paper. Draw a separate coordinate system for each equation.

http://www.flvs.net/products_services/2005_showcase_flvs/math/alg1/lessons/05_07c.htm

How well did you do in the exercises? If you think you need to review some more on graphing linear equations, click on this website address:

http://www.flvs.net/products_services/2005_showcase_flvs/math/alg1/lessons/05_07a.htm

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Going back to the map given by your teacher, can you now try to find the hometowns of Lito, Nelia, Lucy and Mitoy by graphing the linear equations on the map? Use a pencil in drawing the lines.

After you have graphed the equations and you have determined the hometowns of the four friends, try this short QUIZ.

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REFLECTIVE LOG

1. Whose hometown was easiest to find? Why? ______________________________________________________________________________________________________________________________________

2. Whose hometown was the most difficult to find? Why? ______________________________________________________________________________________________________________________________________

3. What steps did you have to do to find Mitoy’s hometown?

Step 1:_____________________________________________________

Step 2: _____________________________________________________

Step 3:_____________________________________________________

Step 4:_____________________________________________________

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SOLVING THE HOMETOWN PUZZLER

Now that you are sure of your answers, graph the equations again on the map to show that you have indeed solved the puzzle. Use colored ink or crayons and label each line accordingly. This is your final output.

(The rubrics for grading are on the next page)

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Criteria for Grading

Excellent 91 – 100

Very Good85 - 88

Acceptable75 - 82

Developing70 - 72

Student’s Rating

Teacher’s Rating

Correctness of the graph

50%

All four lines are plotted correctly. (47 – 50)

Three lines are plotted correctly.(45 – 46)

Two lines are plotted

correctly.(42 – 44)

Only one or none of the

lines are plotted

correctly.(40 – 41)

Accuracy of the Lines

30 %

All four lines very clearly

pass through the black dots representing

the hometowns. (27 – 30)

Three lines very clearly

pass through the black dots representing

the hometowns.

(25 – 26)

Two lines very clearly pass through the black dots

representing the

hometowns. (22 – 24)

Only one or none of the lines pass

through the black dots

representing the

hometowns.(20 – 21)

Neatness and Attractiveness

20%

Exceptionally neat, and

attractive. A different color is used for each line to show

distinctiveness. A ruler was

used in drawing the lines. (17 – 20)

Neat and relatively

attractive. A ruler and was

used in drawing the

lines. (15 – 16)

Lines are neatly drawn but the graph appears quite

plain. (11 – 14)

Appears messy and

looks like done in a hurry. Lines are

visibly crooked.

(10)

Total Score:

Total Score: