�ݺ�ߣ

What is a Line?
• A line is the set of points forming a straight
path on a plane
• The slant (slope) between any two points on
a line is always equal
• A line on the Cartesian plane can be
described by a linear equation
x-axis
y-axis

Definition - Linear Equation
• Any equation that can be put into the form
Ax + By  C = 0, where A, B, and C are
Integers and A and B are not both 0, is called
a linear equation in two variables.
• The graph will be a straight line.
• The form Ax + By  C = 0 is called general
form (Integer coefficients all on one side = 0)

Slope
Slope describes the
direction of a line.

Slope (m)
• It is describes the steepness of the
line. It is also the ratio of rise to
run.
1
2
1
2
x
x
y
y
x
in
change
y
in
change
run
rise
slope






Example 1:
Calculate the slope between (-3, 6) and (5, 2)
1
2
1
2
x
x
y
y
m



)
3
-
(
)
5
(
)
6
(
)
2
(



m
8
4
-

2
1
-

x1 y1 x2 y2
We use the letter m
to represent slope
m

x-axis
y-axis
Find the slope between (-3, 6) and (5, 2)
Rise
Run
-4
8
-1
2
= =
(-3, 6)
(5, 2)
m =

From this result, we can see that...
•If the line falls to the
right, the slope is
negative.

Example 2:
Calculate the slope between (2, 5) and (0, 1)
1
2
1
2
x
x
y
y
m



x1 y1 x2 y2
We use the letter m
to represent slope
m

x-axis
y-axis
Find the slope between (2, 5) and (0, 1)
Rise
Run
-4
-2
2
= =
(2, 5)
(0, 1)
m =

From this result, we can see that...
•If the line falls to the
left, the slope is
positive.

Example 3:
Find the slope between (5, 4) and (5, 2).
1
2
1
2
x
x
y
y
m



)
5
(
)
5
(
)
4
(
)
2
(



m
0
2
-

STOP
This slope is undefined.
x1 y1 x2 y2

x
y
Find the slope between (5, 4) and (5, 2).
Rise
Run
-2
0
Undefined
= =

Example 4:
Find the slope between (5, 4) and (-3, 4).
1
2
1
2
x
x
y
y
m



)
5
(
)
3
-
(
)
4
(
)
4
(



m
8
-
0

This slope is zero.
x1 y1 x2 y2
0


x
y
Rise
Run
0
-8
Zero
= =
Find the slope between (5, 4) and (-3, 4).

From these results we
can see...
•The slope of a vertical
line is undefined.
•The slope of a
horizontal line is 0.

Find the Slopes
(5, -2)
(11, 2)
(3, 9)
1
2
1
2
x
x
y
y
m



3
11
9
2
1



m
Yellow
5
11
)
2
-
(
2
2



m
Blue
3
5
9
2
-
3



m
Red
8
7
-

3
2

2
11
-


Sign of the Slope
Which have a
positive slope?
Green
Blue
Which have a
negative slope?
Red
Light Blue
White
Undefined
Zero
Slope

Summary
• Vertical line
– Slope is undefined
– x-intercept is (x, 0)
– no y-intercept
• Horizontal line
– Slope is 0.
– y-intercept is (0, y)
– no x-intercept

�ݺ�ߣ

FINDING FOR THE SLOPE OF A LINE .ppt

Recommended

More Related Content

Similar to FINDING FOR THE SLOPE OF A LINE .ppt (20)

Recently uploaded (20)

FINDING FOR THE SLOPE OF A LINE .ppt