Republic of the Philippines Department of Education
Region VII, Central Visayas
Division of Cebu Province
SELF-LEARNING HOME TASK (SLHT)
Subject: Mathematics
Grade: 8
Quarter: 2
MELC: illustrates and finds the slope of a line given two-points, equation, and graph
Competency Code: M8AL-Ie-5
Objectives:
Knowledge
: define the slope
Skills
: solve for the slope of a line using the given two points, equation and graph
Values / Attitude: observe accuracy in applying slope in real-life situations
Subject Matter
: Slope of the line
Procedure:
A. Readings/Discussions
Shown at the right is the picture of Mount Mayon. It is one of the
fascinating volcanoes in the Philippines because of its almost
symmetrical conical shape. The approximate steepness of the volcano
is labelled by the line.
The slope of the line can be used to describe how steep Mount Mayon
is.
A line can be describe by its steepness or slope. The slope m of a line
can be computes by finding the qoutient of the rise and the run. That is,
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
𝑚=
slope
The rise refers to the vertical change or change in y-coordinate while the run is the horizintal change or
change in x-coordinate.
𝑚=
𝑟𝑖𝑠𝑒
𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 − 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒
=
=
𝑟𝑢𝑛 ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 − 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒
The slope m of the line passing through two points 𝑃1 (𝑥1 , 𝑦1 ) 𝑎𝑛𝑑 𝑃2 (𝑥2 , 𝑦2 ) is given by
𝑚=
𝑦2 − 𝑦1
𝑦1 − 𝑦2
𝑜𝑟 𝑚 =
, 𝑤ℎ𝑒𝑟𝑒 𝑥1 ≠ 𝑥2
𝑥2 − 𝑥1
𝑥1 − 𝑥2
Examples:
a. Two-points
b. Graphs
c. Equation
A. Finding the slope in given two-points:
Suppose we take two arbitrary points (0,-2) and (3,2).
Solution:
a. Assign values for (𝑥1 , 𝑦1 ) 𝑎𝑛𝑑 (𝑥2 , 𝑦2 )
(0,-2) and (3, 2).
𝑦2
𝑥1
𝑦1
𝑥2
b. Substitute to the formula
c. Compute: 𝑚
4
d. 𝑚 = 3
=
𝑦2 −𝑦1
𝑥2 −𝑥1
=
𝑚=
2−−2
3−0
𝑦2 −𝑦1
𝑥2 −𝑥1
2+2
4
3
3
=
=
B. Finding the slope in a given graph:
The line passes through points (0,1) and (-1, -3).
Moving from 𝑃1 𝑡𝑜 𝑃2 , the rise, or the difference
between the y-coordinates is -3 – 1 = -4. The run
difference between x-coordinates is -1 – 0 = -1. So,
the slope is -4/-1 or 4.
Note:
 The slope of a horizontal line is zero,
while undefined in vertical line.
 The value of the slope 𝑚 tells the trend of
the graph.
If 𝑚 is positive, then the graph is
increasing from the left to right.
If 𝑚 is negative, then the graph is
decreasing from left to right.
If 𝑚 is zero, the the graph is a
horizontal line.
If 𝑚 is undefined, then the graph is
a vertical line.
C. Finding the slope in a given equation.
The figure above shows the graph of the equation 𝒚 = 𝟒𝒙 + 𝟏.
Solution:
The slope-intercept Form is 𝒚 = 𝒎𝒙 + 𝒃, where 𝑚 is the slope and 𝑏 is the y-intercept.
In the given equation the slope is 4. Why?
𝒚 = 𝟒𝒙 + 𝟏
y-interccept
Slope (m)
B. Exercises/Activities:
Find the slope the following given:
1.
(1, 2) and (3, 4)
2.
(5, 6) and ( 0, 11)
3.
5. 𝒚 = 𝟖𝒙 + 𝟐
6. 𝒚 = −𝟑𝒙 + 𝟓
4.
4.
C. Assessment/Application/Outputs (Please refer to DepEd Order No. 31, s. 2020)
1. Find the slope of the line with the equation y = 2x + 4?
a. 2
b. -2
c. 4
d. -4
2. How will you solve for the slope of a line given two points?
a. solve for the change in y over change in x
b. solve for the change in x over a change in y
c. solve for the change in y multiplied by the change in x
d. solve for the change in x multiplied by the change in y
3. Which of the following equations is the steepest?
a. y = 2x + 6
b. y = 4x + 2
c. y = 5x + 1
d. y = 7x + 2
4. Which of the following equations has a slope equal to -10?
a. y = -10x + 4 b. y = 3x + 10
c. y = -2x + 4
d. y = 7x + 9
5. What is the slope of the graph shown at the right?
a. 0
b. 1
c. 2
d. undefined
6. What is the slope of the line with the points (0, 1) (1, 0)?
a. -1
b. 1
c. 2
d. -2
7. What is the graph of a line with a slope equal to 0?
a. increasing from left to right
b. decreasing from left to right
c. horizontal line
d. vertical line
8. Which of the following graphs has a negative slope?
.
9. Which of the following equations has the slope equal to 3?
a. y = 4x + 3
b. y = 3x + 2
c. y = -3x + 5
d. y = x+ 5
10. In the slope-intercept form, y = mx + b, what letter represents the slope of a line?
a. m
b. y
c. b
d. x
References:
DepEd Mathematics Teacher’s Guide 8. pp.162 - 170
DepEd Mathematics Learners Module 8, pp. 182 – 186
DepEd Cebu Province - Mathematics Module 9
Prepared by
JENNILYN S. COLLAMAT
Teacher 1, Langin National High School
Verified by:
MA. LOURDES T. CABONILAS
Principal 1
GUIDE
For the Teacher: You may give other exercises/reinforcement activities other than the ones
provided for in this SLHT.
For the Learner: Please read carefully the key points/readings and follow correctly directions in
accomplishing exercises/tasks.
For the Parent/Home Tutor: Kindly guide learner in accomplishing this home task. Should you need
assistance, you may contact the subject teacher to address questions or give
clarifications/discussions.
Republic of the Philippines Department of Education
Region VII, Central Visayas
Division of Cebu Province
SELF-LEARNING HOME TASK (SLHT)
Subject: Mathematics
Grade: 8
Quarter: 2
MELC: illustrates and finds the slope of a line given two-points, equation, and graph
Competency Code: M8AL-Ie-5
Name: ______________________________
Section: ________________________
Answer Sheet
(Return this paper only)
B. EXERCISES/ACTIVITIES
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6.
C. ASSESSMENT/APPLICATION/OUTPUTS
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