

Illustrating the Slope of a Line
Presentation
•
Mathematics
•
12th Grade
•
Easy
Nelmie Ann Bacaoco
Used 6+ times
FREE Resource
41 Slides • 18 Questions
1
Illustrating the Slope of a Line
Mathematics 8
2
Learning Targets
I can describe the slope of a line;
I can determine the slope of a line given two points, an equation, and a
graph; and
I can reflect on the relevance of the slope of a line in real-life setting.
Mathematics 8
Illustrating the Slope of a Line
3
Essential Question
How can knowledge of slope describe real-world situations and solve real-life problems?
Mathematics 8
Illustrating the Slope of a Line
4
Open Ended
What do you wonder about today's topic?
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Slope of a Line
Mathematics 8
Illustrating the Slope of a Line
6
Review
Mathematics 8
Illustrating the Slope of a Line
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Fill in the Blanks
Type answer...
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Fill in the Blanks
Type answer...
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Fill in the Blanks
Type answer...
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Open Ended
Did you find difficulty in describing the locations of the points?
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Open Ended
Looking back at the graph, are points A and M vertically aligned?
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Open Ended
What is the distance between points A and M?
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Open Ended
Name all pairs of vertically aligned points and determine the distance
between the two vertically aligned points.
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Open Ended
Are points A and I horizontally aligned?
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Open Ended
What is the distance between points A and I?
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Open Ended
Name all pairs of horizontally aligned points and determine the distance
between the two horizontally aligned points.
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Open Ended
What is the ratio of the vertical distance of points A and M to the
horizontal distance of A and I?
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Open Ended
If you connect points M and I, you will form a slant line. The slant of a
line is referred to as the slope of a line. What is a slope of a line?
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Multiple Choice
Situation 1: Teacher Carlo is travelling to two different hilly roads.
Which road is difficult to drive?
Road 1
Road 2
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Multiple Choice
Situation 2: After reaching the top of the hilly roads, Teacher Carlo needs to
drive down the hilly roads.
Which road will build up speed?
Road 3
Road 4
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Open Ended
Situation 3. After moving down the hill, Teacher Carlo is now driving on a flat
ground.
Do you think he can send text message to his friends? Why? Why not?
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Open Ended
Situation 4. Is it possible for Teacher Carlo to drive like the illustrations
below? Why?
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Slope
The slope, represented by 𝒎, is defined as the ratio of the vertical change between two points
to the horizontal change between the same two points. The vertical change is referred to as the rise and the horizontal change as the run.
Mathematics 8
Illustrating the Slope of a Line
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Slope (m)
Mathematics 8
Illustrating the Slope of a Line
m = rise / run
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Slope (m) - Road 1
Mathematics 8
Illustrating the Slope of a Line
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Slope (m) - Road 2
Mathematics 8
Illustrating the Slope of a Line
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Slope (m)
Mathematics 8
Illustrating the Slope of a Line
The slope is positive. Take note that the steeper the hilly road that
Teacher Carlo drives, the larger is the slope.
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Slope (m) - Road 3
Mathematics 8
Illustrating the Slope of a Line
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Slope (m) - Road 4
Mathematics 8
Illustrating the Slope of a Line
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Slope (m)
Mathematics 8
Illustrating the Slope of a Line
The slope is negative. The steeper the road, the more the car builds up speed, and the more the slope
becomes negative.
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Slope (m) - Road 5
Mathematics 8
Illustrating the Slope of a Line
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Slope (m)
Mathematics 8
Illustrating the Slope of a Line
Is Teacher Carlo free to send text messages to anyone? The answer is NO.
Republic Act No. 10913 known as the Anti-Distracted Driving Act prohibits distracted driving by restricting and penalizing
the use of mobile phones and other electronic devices while
driving on any public thoroughfare, highway or street in the Philippines.
The slope in road 4 and road 5 is 0.
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Slope (m) - Road 5
Mathematics 8
Illustrating the Slope of a Line
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Slope (m) - Road 5
Mathematics 8
Illustrating the Slope of a Line
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Slope (m)
Mathematics 8
Illustrating the Slope of a Line
The slope in road 6 is undefined.
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Multiple Choice
Given the graph, what is the slope of the line?
1
2
4
8
37
Finding the Slope of a Line Given Two Points
Mathematics 8
Illustrating the Slope of a Line
38
Finding the Slope of a Line Given Two Points
Mathematics 8
Illustrating the Slope of a Line
A (5,1) and B (7,9)
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Finding the Slope of a Line Given Two Points
Mathematics 8
Illustrating the Slope of a Line
If A is the first point, what is its abscissa (or 𝑥1)? What about its ordinate
(or 𝑦1)?
Solution:
𝑥1 = 5
𝑦1 = 1
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Finding the Slope of a Line Given Two Points
Mathematics 8
Illustrating the Slope of a Line
If B is the second point, what is its abscissa (or 𝑥2)? What about its ordinate (or
𝑦2)?
Solution:
𝑥2 = 7
𝑦2 = 9
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Finding the Slope of a Line Given Two Points
Mathematics 8
Illustrating the Slope of a Line
What is the difference of the ordinates (or y-coordinates) of points A and B? What about the difference of the abscissas
(or x-coordinates) of points A and B?
Solution:
𝑦2 − 𝑦1 = 9 − 1 = 8
𝑥2 − 𝑥1 = 7 − 5 = 2
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Finding the Slope of a Line Given Two Points
Mathematics 8
Illustrating the Slope of a Line
Compare the difference of the values of y (the ordinates) to the rise on the graph. What have
you observe?
Solution:
𝑦2 − 𝑦1 = 𝑟𝑖𝑠𝑒
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Finding the Slope of a Line Given Two Points
Mathematics 8
Illustrating the Slope of a Line
Compare the difference of the values of x (the abscissas) to the run on the graph. What have
you observe?
Solution:
𝑥2 − 𝑥1 = 𝑟𝑢𝑛
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Finding the Slope of a Line Given Two Points
Mathematics 8
Illustrating the Slope of a Line
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Finding the Slope of a Line Given Two Points
Mathematics 8
Illustrating the Slope of a Line
Given two points, (x1, y1) and (x2, y2) the slope of the line can be solved using
the formula:
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Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
The slope of a line can sometimes be quickly determined from its
equation.
For example:
4x-y=19
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Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
4x-y=19
1. Is the equation written in the form 𝐴𝑥 + 𝐵𝑦 = 𝐶?
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Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
4x-y=19
1. Is the equation written in the form 𝐴𝑥 + 𝐵𝑦 = 𝐶?
The answer is YES.
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Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
4x-y=19
2. What are the values of the coefficients A and B?
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Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
4x-y=19
2. What are the values of the coefficients A and B?
Solution: 𝐴 = 4 𝐵 = −1
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Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
4x-y=19
3. What is the additive inverse of the coefficient 𝐴?
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Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
4x-y=19
3. What is the additive inverse of the coefficient 𝐴?
Solution: Since 𝐴 is 4 then the – 𝐴 is −4
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Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
4x-y=19
4. Get the ratio of the coefficient of the additive inverse 𝐴 to the coefficient of 𝐵.
54
Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
4x-y=19
4. Get the ratio of the coefficient of the additive inverse 𝐴 to the coefficient of 𝐵.
Solution: −𝐴 /𝐵 = −4 /−1 = 4
55
Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
4x-y=19
5. What have you observed? Is the ratio of the rise to the run, the ratio of the differences in 𝑦 − values to the differences in the 𝑥 − values, the same with the ratio of the additive inverse of 𝐴 to 𝐵?
56
Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
4x-y=19
5. What have you observed? Is the ratio of the rise to the run, the ratio of the differences in 𝑦 − values to the differences in the 𝑥 − values, the same with the ratio of the additive inverse of 𝐴 to 𝐵?
57
Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
58
Finding the Slope of a Line Given an Equation
Mathematics 8
Illustrating the Slope of a Line
Take note:
The slope can be positive, negative, zero, or undefined.
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Learning Targets
I can describe the slope of a line;
I can determine the slope of a line given two points, an equation, and a
graph; and
I can reflect on the relevance of the slope of a line in real-life setting.
Mathematics 8
Illustrating the Slope of a Line
Illustrating the Slope of a Line
Mathematics 8
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