ObjectivesThe student will be able to:

1. find the slope of a line given two points and a graph.

2. illustrate the slope of a line using two points and the slope of a line in a graph.

3. apply slope of a line in real-life situations.

ACTIVITY

1. Icy Road Ahead

2. Steep Road Ahead3. Curvy Road Ahead4. Truck Entering

Highway Ahead

What is the meaning of this sign?

What does the 7% mean?

7% is the slope of the road. It means the road drops 7 feet

vertically for every 100 feet horizontally.

7%

So, what do you mean steepness of a line???SLOPE

7 feet

100 feet

What to do…1. The class will be divided into 4 groups.

Each group will be given graphing paper and marker for the activity.

2. Each group must plot the pair of points of the item assigned to them in a coordinate plane. Then, they will complete the table.

3. After the group has done, select a reporter of the group.

Complete the table. Plot the points.Group Points x y Slope

Group 1 (-3,5)(-3,-2)

Group 2 (3,5)(-1,4)

Group 3 (2,0)(0,4)

Group 4 (1,4)(2,4)

ANALYSIS

1. How did you find the activity?

2. How did you get the slope of a line?

3. Did you find it difficult to solve for the slope? Why?

Answer the following:

Making conjectures:If the slope of a line is positive, then ____________________________.If the slope of a line is negative, then ____________________________.If the slope of a line is zero, then ____________________________.If the slope of a line is undefined, then ____________________________.

ABSTRACTION

Slope can be expressed different ways:

A line has a positive slope if it rises from left to right. A line has a negative slope if it rises from right to left.

2 1

2 1

( ) vertical change

( ) horizontal change

y y risem

x x run

When given the graph, it is easier to apply “rise over run”.

1) Determine the slope of the line.

Start with the lower point and count how much you rise and run to get to the other

point!

Determine the slope of the line.

6

3

run36

= =1

2

rise

Notice the slope is positive AND the line increases!

2) Find the slope of the line that passes through the points (-2, -2) and (4, 1).

(1 ( 2))

(4 ( 2))m

2 1

2 1

( )

( )

y ym

x x

(1 2)

(4 2)

When given points, it is easier to use the formula!

y2 is the y coordinate of the 2nd ordered pair (y2 = 1)

y1 is the y coordinate of the 1st ordered pair (y1 = -2)

13

6 2

Did you notice that Example #1 and Example #2 were the same problem written differently?

(-2, -2) and (4, 1)6

31

2slope

You can do the problems either way!Which one do you think is easiest?

3) Find the slope of the line that goes through the points (-5, 3) and (2, 1).

m y2 y1

x2 x1

1 3

2 ( 5)m

1 3

2 5m

2

7m

Determine the slope of the line.

The line is decreasing (slope is negative).

2

-1

rise

run

2

1 2

Find points on the graph. Use two of them and apply rise over run.

What is the slope of a horizontal line?

The line doesn’t rise!

m 0

number0

All horizontal lines have a slope of 0.

What is the slope of a vertical line?

The line doesn’t run!

All vertical lines have an undefined slope.

m number

0undefined

Performance TaskThe teacher asks the students to

perform a task. Each group must make a race track.

This is adopted in the game show Minute to Win It. Wherein, each group must discover how do they make the ball (jolen) reached the finish line using staple wires.

APPLICATION

GOAL: Each group must discover how can they make the ball travelled through the finish line using staple wires.ROLE: To perform a taskAUDIENCE: Subject Teacher and StudentsSITUATION: The teacher asks the students to perform a task.PRODUCT: Race trackSTANDARDS: Stability and Difficulty

CRITERIA 4 3 2 1Stability The track

will not collapse until the jolen reach the finish line.

The track will collapse but the jolen reach the finish line.

The track will not collapse but the jolen did not reach the finish line.

The track collapse and the jolen not reach the finish line.

Difficulty The track shows three or more than three slopes.

The track shows two slopes.

The track shows one slope.

The track shows no slope.

Complete the table. Plot the points.Group Points x y Slope

Group 1 (2,1)(-5,0)

Group 2 (1,0)(0,3)

Group 3 (2,4)(2,-2)

Group 4 (-6, 1)(-1,1)

• “Math is like a puzzle, at first you will not understand and appreciate. But as you indulge yourself into it, you will be able to see its beauty and wonders… And you will realize that everything about it is true and exact – for as long as you have a logical and critical mind!”

• -ANONYMOUS-