1.
MELC: At the end of the lesson, the learners
should be able to:
SLOPE OF A LINE
1. illustrate and find the slope of a line given two points;
2. illustrate and find the slope of a line given its graph.

2.
+
-ain
Mount Mayon
+

3.
+
Chocolate Hills
-C

4.
+
Mount Everest
+
-ain -ready -ba

5.
+
Rice Terraces
+

6.
+
Stairway

7.
SLOPE OF A LINE

8.
The slope of a line is the measure
of the steepness and the direction
of the line.
It is defined as the change in y
coordinate with respect to the
change in x coordinate of that
line.

9.
 The graph of linear equations is a straight line; it has
a constant slope.
Slope of a line (m)
m =
𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒓𝒊𝒔𝒆
𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝒓𝒖𝒏
;
m =
𝒔𝒕𝒆𝒆𝒑𝒏𝒆𝒔𝒔
𝒅𝒊𝒓𝒆𝒄𝒕𝒊𝒐𝒏
;
m =
𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
m =
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒚
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒙
; m =
∆𝒚
∆𝒙
𝒍𝒊𝒏𝒆 𝑨
𝒍𝒊𝒏𝒆 𝑩
Line A is steeper than
Line B

10.
FINDING THE SLOPE OF A LINE:
a. given two points
m =
𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
where m= slope
𝑥1, 𝑦1 - coordinate of one point
𝑥2, 𝑦2 - coordinate of another
point
Find the slope of a line passing
through points ( 1, 3) and ( 5, 6 )
𝒚𝟏 𝒚𝟐
𝒙𝟐
𝒙𝟏
m =
𝒚𝟐 − 𝒚𝟏
𝒙𝟐 − 𝒙𝟏
m =
𝟑
𝟒
𝟓
𝟔 − 𝟑
− 𝟏

11.
Find the slope of a line
passing through points
( -5, -3) and ( 4, 1 )
𝒚𝟐
𝒙𝟏 𝒙𝟐
𝒚𝟏
m =
𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
𝟏 −(-3)
𝟒−(-5)
𝟏 + 𝟑
𝟒 + 𝟓
𝟒
𝟗
Find the slope of a line
passing through points
( 2, 2) and ( -1, -3 )
𝒙𝟏 𝒙𝟐 𝒚𝟐
𝒚𝟏
m =
𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
−𝟑 −𝟐
−𝟏− 𝟐
−𝟓
−𝟑
POSITIVE SLOPE
The line RISES from left to right

12.
Find the slope of a line
passing through points
( -3, 4) and ( 3, -2 )
𝒚𝟐
𝒙𝟏 𝒙𝟐
𝒚𝟏
m =
𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
−𝟐 − 4
𝟑 − (-3)
− 𝟔
𝟑 + 𝟑
−𝟔
𝟔
Find the slope of a line
passing through points
( 2, 5) and ( 6, 2 )
𝒙𝟏
𝒙𝟐 𝒚𝟐
𝒚𝟏
m =
𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
−𝟑
𝟒
NEGATIVE SLOPE
The line FALLS from left to right
𝒐𝒓 − 𝟏
𝟐 − 𝟓
𝟔 − 𝟐

13.
Find the slope of a line
passing through points
( 5, 4) and ( 5, -2 )
𝒚𝟐
𝒙𝟏 𝒙𝟐
𝒚𝟏
m =
𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
−𝟐 − 4
𝟓 − 5
− 𝟔
𝟎
Find the slope of a line
passing through points
( -1, 5) and ( -1, -2 )
𝒙𝟏 𝒚𝟐
𝒚𝟏
m =
𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
−𝟐−𝟓
−𝟏 −(−𝟏)
−𝟕
−𝟏 + 𝟏
UNDEFINED or NO SLOPE
The line is VERTICAL and
is parallel to the y-axis
m = 𝒖𝒏𝒅𝒆𝒇𝒊𝒏𝒆𝒅 𝒐𝒓
𝑵𝑶 𝑺𝑳𝑶𝑷𝑬
−𝟕
𝟎
m = 𝒖𝒏𝒅𝒆𝒇𝒊𝒏𝒆𝒅 𝒐𝒓
𝑵𝑶 𝑺𝑳𝑶𝑷𝑬
𝒙𝟐

14.
Find the slope of a line
passing through points
( -3, -3) and ( 5, -3 )
𝒚𝟐
𝒙𝟏 𝒙𝟐
𝒚𝟏
m =
𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
−𝟑−(-3)
𝟓 − (-3)
+ 𝟑
𝟓 + 𝟑
𝟎
𝟖
Find the slope of a line
passing through points
( -2, -2) and ( 4, -2 )
𝒙𝟏 𝒙𝟐
𝒚𝟐
𝒚𝟏
m =
𝒚𝟐−𝒚𝟏
𝒙𝟐−𝒙𝟏
−𝟐−(−𝟐)
𝟒 − (−𝟐)
−𝟐
𝟒
ZERO SLOPE
𝒐𝒓 𝟎
−𝟑
The line is HORIZONTAL and is
parallel to the x - axis
+ 𝟐
+ 𝟐
𝟎
𝟔
𝒐𝒓 𝟎

15.
Figure A Figure B
Figure C
Rising from left to right
Horizontal line parallel
to the x-axis
Falling from left to right
Figure C
Figure A
Figure B
Figure D
Vertical line parallel to
the y-axis
Figure D
POSITIVE SLOPE
NEGATIVE SLOPE
UNDEFINED SLOPE
ZERO SLOPE

16.
Let’s Sing and Dance
To the right, to the right,
POSITIVE SLOPE
To the left, to the Left,
NEGATIVE SLOPE
Horizontal, ZERO
Vertical, UNDEFINED…

17.
SEATWORK
1. Find the slope of a line passing
through points ( 3, 1) and ( 5, 4).
Graph the line.
2. Find the slope of a line passing
through points ( 6, 2) and ( 6, 5).
Graph the line.