Transcript Slope of Line

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 us how much the line rises from one
point to another located one unit to the right.
Rise
1 unit
Examples :
1 unit
Slope = 2
½
or 0.5
of a unit
1 unit
2 units
1 unit
Slope = 1
1 unit
Slope =
½
0r 0.5
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EXERCISES :
1)
A. Using only the concept of slope and a ruler, find the slope of the following lines:
Slope =
Slope =
B.Using only the concept of slope and a ruler draw lines with the following slopes:
Slope = 3
Slope = ¼ 0r 0.25
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2)
A. Using the concept of slope and the grid find the slope of the following lines:
Slope =
Slope =
B. Using the concept of slope and the grid draw lines with the following slopes:
Slope = 2
Slope = 2.5
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+
_
Positive: When the line actually rises or goes up.
Negative: When instead of rising, the line goes down.
Example:
Positive Slope
2 units
going up
Moving
left to Right
Negative Slope
1 unit
2 units going
down or
-2
1 unit
Slope = 2 or +2
Slope = - 2
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EXERCISES :
1. Indicate the sign of
2. Find the slope of
the slope for each line
shown below.
the following lines.
3. What is the slope of the
line in the graph? Choose
the best answer.
Slope =
Use a
ruler
Slope =
a)
b)
c)
d)
e)
½
2
-2
-½
1/3
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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.
Y2
Y1
1 unit
X2
X1
Definition :
Slope
Vertical Distance
y
=
=
=
Horizontal Distance
x
Then, there are two ways to find the slope of a line:
 Use a graph to find
 Use the formula.
x and
y
Y2 –Y1
X2 – X1
GED Formula
and find the ratio; or
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Steps:
y
1.- Use the graph to choose a
x and a y
with lengths that have an exact number of
units.
2.- Slope =
x
y/
y
Example :
In the graph:
x
x= 4
and
y = 5, then the
=
Slope =
x
5
4
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EXERCISES:
(From the book: GED Mathematics . Steck-Vaughn)
Find the slope of each line
1.
y
y
2.
3.
y
x
x
x
Slope =
Slope =
y
4.
Slope =
5. The line that passes through the points: (1,-3) and (0,1).
y
Note: Draw the line and
find the slope using the graph
x
x
Slope =
Slope =
9
Y2
Point
Formula :
2
Point 1 = (X1,Y1)
Y1
Point
Y2 –Y1
X2 – X1
Point 2 = (X2,Y2)
1
If the coordinates of two points are given, we do not
need the graph to use the Slope Formula.
X1
Example :
X2
In the graph : Point 1 = ( 2 , 4 ) and Point 2 = ( 9 , 8 )
X1 Y1
Then,
Slope =
Y2 –Y1
X2 – X1
X2 Y2
8 – 4
=
4
=
9 – 2
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EXERCISES:
(From the book: GED Mathematics . Steck-Vaughn)
Find the slope of the line that passes through each pair of points.
1. (4,5) and (3,- 4)
4. The points are shown in the graph
y
x
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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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.
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
At the end, discuss which method won more times and why.
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 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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