slope of a line prepared by gladys g. poma. concept : the slope of a straight line is a number that...

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Slope of a Line Prepared by Gladys G. Poma

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Page 1: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

Slope of a Line

Prepared by Gladys G. Poma

Page 2: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

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 :

1 unit

Slope = 2 Slope = 1 Slope = ½ 0r 0.5

2 units

1 unit

1 unit

1 unit

½ or 0.5 of a unit

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Page 3: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

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 0r 0.25

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Page 4: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

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

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Page 5: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

1 unit

Slope = 2 or +2

2 units going up

Example: Positive Slope Negative Slope

2 units going down

or -2

1 unit

Slope = - 2

++__

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

Movingleft to Right

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Page 6: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

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

Use aruler

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Page 7: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

The slope indicates rise per unit of horizontal right 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 : 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.

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Page 8: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

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 the Slope = x

y=

5

4

Example :

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Page 9: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

EXERCISES: Find the slope of each line

(From the book: GED Mathematics . Steck-Vaughn)

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

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Page 10: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

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

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Page 11: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

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

(From the book: GED Mathematics . Steck-Vaughn)

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)

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Page 12: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

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 writes 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, discuss which method won more times and why.

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Page 13: Slope of a Line Prepared by Gladys G. Poma. Concept : The slope of a straight line is a number that indicates the steepness of the line. The slope tells

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.

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