Prepared by Gladys G. Poma

Concept of slope Sign of the slope Find the slope using a graph Find the slope using the formula Classroom activity Conclusions and additional Information

Introduction…..

Concept :The slope of a straight line is a number that indicates the steepness of the line.The slope tells us how much the line rises from one point to another located one unit to the right.

1 unit

Rise

Examples :

Slope = 2 Slope = 1 Slope = ½ 0r 0.5

1 unit

2 unit

1 unit

1 unit

1 unit

½ or 0.5 unit

A. Using only the concept of slope and a ruler, find the slope of the following lines:

B. Using only the concept of slope and a ruler draw lines with the following slopes:

EXERCISES :

1)

Slope = Slope =

Slope = 3 Slope = ¼ or 0.25

A. Using only the concept of slope and a ruler, find the slope of the following lines:

B. Using only the concept of slope and a ruler draw lines with the following slopes:

EXERCISES :

1)

Slope = 1.5 Slope = 0.3

Slope = 3 Slope = ¼ or 0.25

1 cm.1.5 cm. 0.3 cm.

1 cm.

1 cm.

3 cm.0.25 cm.

1 cm.

A. Using the concept of slope and the grid find the slope of the following lines:

B. Using the concept of slope and the grid draw lines with the following slopes:

Slope =

2)

Slope = 2.5

Slope =

Slope = 2

A. Using the concept of slope and the grid find the slope of the following lines:

B. Using the concept of slope and the grid draw lines with the following slopes:

Slope = 1

2)

Slope = 2.5

Slope = 4

Slope = 2

Introduction…..

Slope = 2 or +2

2 units going up

Example: Positive Slope Negative Slope

2 units going down

or -2

Slope = - 2

++__

Positive: When the line actually rises or goes up.Negative: When instead of rising, the line goes down.

Movingleft to Right

1 unit

1 unit

1. Indicate the sign of the slope for each line shown below.

2. Find the slope of the following lines.

Slope =

EXERCISES :

Slope =

3. What is the slope of the line in the graph? Choose the best answer.

a)½b) 2c) -2d)- ½e) 1/3

1. Indicate the sign of the slope for each line shown below.

2. Find the slope of the following lines.

Slope = - 3

EXERCISES :

Slope = - 1.5

3. What is the slope of the line in the graph? Choose the best answer.

a)½b) 2c) -2d)- ½e) 1/3

+

+

1 cm.

1.5 cm.

Introduction…..

yx

=Horizontal Distance

Vertical Distance

Y2 – Y1==

X2 – X1Slope

1 unit

Y2

Y1

X1 X2

GED FormulaThen, there are two ways to find the slope of a line: Use a graph to find x and y and find the ratio; or Use the formula.

The slope indicates rise per unit of right horizontal movement and this value is the same everywhere along the line, because the line is straight. Then, if we move more than one unit to the right, the rise will be proportional. That is why, to find the slope we can use any two points on the line and find the ratio of their vertical distance to their horizontal distance.

Definition :

x

y

Steps:

1.- Use the graph to choose a x and a

y with lengths that have an exact number of units.

2.- Slope = y / x

In the graph: x = 4 and y = 5, then Slope =

x

y=

5

4

Example :

EXERCISES: Find the slope of each line

Slope = Slope = Slope =

y

x

x

x

yy

Slope =

x

y

1. 2. 3.

4. 5. The line that passes through the points: (1,-3) and (0,1).

y

x

Slope =

Note: Draw the line and find the slope using the graph

EXERCISES: Find the slope of each line

Slope = -1 Slope = 3/2 or 1.5

Slope = - ½ or –0.5

y

x

x

x

yy

Slope = 1/2

x

y

1. 2. 3.

4. 5. The line that passes through the points: (1,-3) and (0,1).

y

x

Slope = - 4

Note: Draw the line and find the slope using the graph

(1,-3)

(0,1)

Y2

Y1

X1 X2

Point

2

Point

1

Point 1 = (X1,Y1)

Point 2 = (X2,Y2)

If the coordinates of two points are given, we do not need the graph to use the

Slope Formula.

Formula :

Point 1 = ( 2 , 4 ) and Point 2 = ( 9 , 8 )

Y2 – Y1

X2 – X1

X1 Y1

Example :In the graph :

X2 Y2

Then, Y2 – Y1

X2 – X1Slope = =

8 – 4

9 – 2 =

4

7

EXERCISES: Find the slope of the line that passes through each pair of points.

x

y

1. (4,5) and (3,- 4) 4. The points are shown in the graph

2. (- 3,- 3) and (- 2,0)

Use the formula to solve. Suppose you do not know the concept of a slope and the graph method, only the formula.

3. (- 4,3) and (5,3)

EXERCISES: Find the slope of the line that passes through each pair of points.

x

y

1. (4,5) and (3,- 4) 4. The points are shown in the graph

2. (- 3,- 3) and (- 2,0)

Use the formula to solve. Suppose you do not know the concept of a slope and the graph method, only the formula.

3. (- 4,3) and (5,3)

Y2 – Y1

X2 – X1

Slope = 9

= - 4 - 5

3 - 4 =

-9

-1

Y2 – Y1

X2 – X1

Slope = 3

=0 - - 3

- 2 - - 3 =

3

1

Y2 – Y1

X2 – X1

Slope = 0

= 3 - 3

5 - - 4 =

0

9

Y2 – Y1

X2 – X1

Slope = 3 / 5

=2 - - 1

3 - - 2 =

3

5

(3,2) Point 1

(-2,-1) Point 1

Point 1 Point 2

Exercises for the game

1) Two teams : Both teams solve the same exercise, but each team uses a different method. Students work in pairs or independently. The student who finishes first in each team write the solution on the board. The team/method that finishes first wins. Data: Coordinates of two points

2) Same as part 1, but switch methods between teams.Data: Coordinates of two points

3) Similar to part 1, but now each person chooses his or her favorite method .

If everybody chooses the same method, then the students that finish first

in parts 1 and 2 must use the other method. Data: Coordinates of two points

Objective : Compare the two given methods to find the slope: Graph and Formula . The student will work with both methods and choose which one they like better.

At the end, analyze which method won more times and why.

The slope of any horizontal line is 0.

A vertical line has no slope.

All lines with the same slope are parallel.

If we have the equation of a line written in the form: y = mx + b, where m and b are numbers, then m is the slope of the line. Examples : 1) The line with equation y = 3x - 4 has slope 3.

2) The line with equation y = -x + 5 has slope -1.