Grade 8-slope-of-a-line

9. Illustrates the slope of a line. M8AL – If – 9
10. Finds the slope of a line given the graph and two
points. M8AL-Ig-10
SLOPE OF A LINE

On a faraway vast land,
there’s a mystical forest outside
the Kingdom of Albanya.
Florante, son of Duke Briseo
and Princess Floresca, was
knotted tightly on a giant tree
in the middle of the dark forest.

Sadness and
emptiness crept
around the helpless
Prince. The scary
woods and uncanny
sounds of animals
and creatures just
didn’t help.

Just before two huge lions were about to ravish the poor Prince, a
kindhearted Persian Morong, Aladin, helped Florante. Aladin was on exile
from his own kingdom because of his father’s cruelty.

The two became good friends and they started to talk about their
past and what brought them there in the woods. Florante told Aladin
that Adolfo who is his rival to Laura’s heart betrayed him, tortured him,
tied on a tree and kidnapped Laura.

F
Let us help Florante
in finding the exact location
of Laura in the Palace of
Albanya so he could rescue
her. Suppose the coordinates
of the location of Florante
when plotted in a Cartesian
Plane is (2, 1), while Laura
is at point (8, y) and the
slope containing their
location is 1/3.
(2, 1)
(8, y)

Slope
It refers to the steepness of the line.
It is denoted by “m”.
𝒎 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
𝒎 =
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒕𝒉𝒆 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝒎 =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
,
where x1 and y1 are coordinates of P1
x2 and y2 are coordinates of P2

Finding the Slope Given Two Points
B (3, 2) D (- 3, -2)
x1 = 3
y1 = 2
x2 = - 3
y2 = - 2
A B
CD
m =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
m = -2 2-
-3 3-
m = -4
-6
m = 2
3

Finding the Slope Given Two Points
m =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
A (- 3, 2) D (- 3, -2)
x1 = -3
y1 = 2
x2 = - 3
y2 = - 2
A B
CD
m = -2 2-
-3 (-3)-
m = -4
0
m = undefined

FINDING THE SLOPE OF A LINE GIVEN TWO POINTS
STUDENT’S WORKSHEET – MATH BREAKER MAP
Find the slope of the line
passing through points
(3,2) and (5,8)
Perform the operation.
Express Your Answer in
Simplest Form
Substitute the Values in
the FORMULA
Given P1(3,2) and P2(5,8)
Identify the values of
X1, Y1, X2, Y2

(3,2) and (5,8)
Simplest Form
the FORMULA
X1, Y1, X2, Y2
x1 = 3 x2 = 5
y1 = 2 y2 = 8
m =
𝟖 −𝟐
𝟓−𝟑
m =
𝟔
𝟐
= 3

(-3,2) and (1,1)
Given P1(-3,2) and P2(1,1)
X1, Y1, X2, Y2
Simplest Form
the FORMULA

(-3,2) and (1,1)
Given P1(-3,2) and P2(1,1)
X1, Y1, X2, Y2
Simplest Form
the FORMULA
x1 = - 3 x2 = 1
y1 = 2 y2 = 1
m =
𝟏 −𝟐
𝟏−(−𝟑)
m =
−𝟏
𝟒

(1,4) and (5,4)
X1, Y1, X2, Y2
Simplest Form
the FORMULA

(1,4) and (5,4)
X1, Y1, X2, Y2
Simplest Form
the FORMULA
x1 = 1 x2 = 5
y1 = 4 y2 = 4
m =
𝟒 − 𝟒
𝟓 −𝟏
m =
𝟎
𝟓
= 0

(5,2) and (5,6)
X1, Y1, X2, Y2
Simplest Form
the FORMULA
x1 = 5 x2 = 5
y1 = 2 y2 = 6
m =
𝟔 −𝟐
𝟓−𝟓
m =
𝟒
𝟎
= undefined

(5,2) and (5,6)
X1, Y1, X2, Y2
Simplest Form
the FORMULA

C
B
D
A
6 units
4 units
Finding the slope given the graph.
𝐦 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
A B
CD
m =
4
6
m = 2
3

C
B
D
A
- 6 units
- 4 units
𝐦 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
-4
-6
m = 2
3
m =

C
B
D
A
3 units
2 units
𝐦 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
𝐦 =
𝟒
𝟔
𝐦 =
𝟐
𝟑
2 units
3 units
A B
CD

4 units
𝐦 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
𝐦 =
𝟒
𝟎
𝐦 = 𝐮𝐧𝐝𝐞𝐟𝐢𝐧𝐞𝐝
A B
CD

Rise = ___________
FINDING THE SLOPE OF A LINE GIVEN THE GRAPH
Plot and connect the points
A (3 , 2) and B (5 , 8) to
form a line.
From point A to
point B identify :
Run = ___________
From point A to
point B identify :
𝒎 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
= -------
What is the ratio of the
rise and the run? Express
your answer in simplest
form.

Rise = ___________
A (3 , 2) and B (5 , 8) to
form a line.
From point A to
point B identify :
Run = ___________
From point A to
point B identify :
𝒎 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
= -------
form.
2
6
6
2
= 3

Rise = ___________
A (-3 , 2) and B (1 , 1) to
form a line.
From point A to
point B identify :
Run = ___________
From point A to
point B identify :
𝒎 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
= -------
form.

Rise = ___________
A (-3 , 2) and B (1 , 1) to
form a line.
From point A to
point B identify :
Run = ___________
From point A to
point B identify :
𝒎 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
= -------
form.
-4
1
1
-4

Rise = ___________
A (1, 4) and B (5 , 4) to form
a line.
From point A to
point B identify :
Run = ___________
From point A to
point B identify :
𝒎 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
= -------
form.

Rise = ___________
A (1, 4) and B (5 , 4) to form
a line.
From point A to
point B identify :
Run = ___________
From point A to
point B identify :
𝒎 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
= -------
form.
4
0
0
4 = 0

Rise = ___________
A (5 , 2) and B (5 , 6) to
form a line.
From point A to
point B identify :
Run = ___________
From point A to
point B identify :
𝒎 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
= -------
form.

Rise = ___________
A (5 , 2) and B (5 , 6) to
form a line.
From point A to
point B identify :
Run = ___________
From point A to
point B identify :
𝒎 =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
= -------
form.
0
4
4
0
= undefined

Group
Number
Slope Description of
the Slope
Graph Description of the Graph
1
2
3
4
3
-
𝟏
𝟒
0
Undefined
Positive
Slope
Negative
Slope
Zero
Slope
Undefined
Slope
Line rises from
left to right.
Line rises from
right to left.
Line is
horizontal.
Line is vertical.

Given two points or graph, solve the slope of the following, then shade the figure with the
assigned color that corresponds to your answer.
1. (5, 4) and (0, 0) red
2. (6, -2) and (3, -8) yellow
3. (2, 5) and (1, 2) green
4. Blue 5. orange 6. violet

−
6
5
2 23 32 −
6
5
4
54
5
4
54
5
2
2
3
3
−
6
5
−
6
5
7
2
7
2
7
2
7
2
0 0

−
6
5
2 23 32 −
6
5
4
54
5
4
54
5
2
2
3
3
-
6
5
−
6
5
7
2
7
2
7
2
7
2
0 0

Find the exact location of Laura in the Palace of Albanya so Florante could rescue her. The coordinates of the
location of Florante when plotted in a Carthesian Plane is (2, 1), while Laura is at point (8, y) and the slope
containing their location is
𝟏
𝟑
.
Write what are the given facts. Write what is asked on the problem.
Write the formula to be used.
express the answer in a complete statement.
Solve for what is asked.

Find the exact location of Laura in the Palace of Albanya so Florante could rescue her. The coordinates of the
location of Florante when plotted in a Carthesian Plane is (2, 1), while Laura is at point (8, y) and the slope
containing their location is
𝟏
𝟑
.
Write what are the given facts. Write what is asked on the problem.
Write the formula to be used.
express the answer in a complete statement.
Solve for what is asked.
(2,1) – the location of Florante
(8, y) – the location of Laura
𝟏
𝟑
- the slope of their location
Find the exact location of Laura in the palace
m =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
1
3
=
𝑦−1
8 −2
1
3
=
𝑦−1
6
6 (
1
3
=
𝑦−1
6
) 6
2 = y – 1
2+1 = y – 1+1
3 = y or y = 3
The exact location of Laura in the palace is at
point (8,3)

Since Florante knew the exact location of Laura, he
saw Laura safe because she was saved by Princess Flerida
when Adolfo tried to rape her.

Florante and Laura
married each other and celebrated
their wedding, They became the
new King and Queen of Albanya
while Aladin and Flerida were
baptized as Christian before they
get married too.

1. Slope refers to the __________ of the line.
2. The slope of a vertical line is ___________.
3. The slope of ___________ line is 0.
Fill in the blanks.

4. THE SLOPE OF A LINE IS SOMETIMES DEFINED AS RISE
OVER ________.
5. THE SLOPE OF A IS A CHANGE IN _________ DIVIDED
BY THE CHANGE IN _________.
Fill in the blanks.

1. Slope refers to the __________ of the line.
2. The slope of a vertical line is ___________.
3. The slope of ___________ line is 0.
steepness
undefined
horizontal
Fill in the blanks.

4. THE SLOPE OF A LINE IS SOMETIMES DEFINED AS RISE
OVER ________.
5. THE SLOPE OF A IS A CHANGE IN _________ DIVIDED
BY THE CHANGE IN _________.
run
Vertical
distance
Horizontal
Distance
Fill in the blanks.

“ The steeper the mountain the harder the
climb the better the view from the finish
line”. (unknown)

Grade 8-slope-of-a-line

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