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Illustrating the Slope of a Line

Illustrating the Slope of a Line

Assessment

Presentation

Mathematics

12th Grade

Easy

Created by

Nelmie Ann Bacaoco

Used 6+ times

FREE Resource

41 Slides • 18 Questions

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​Illustrating the Slope of a Line

Mathematics 8​

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Learning Targets

  1. I can describe the slope of a line;​

  2. I can determine the slope of a line given two points, an equation, and a

    graph; and

  3. ​I can reflect on the relevance of the slope of a line in real-life setting.

Mathematics 8

Illustrating the Slope of a Line

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Essential Question

How can knowledge of slope describe real-world situations and solve real-life problems?

Mathematics 8

Illustrating the Slope of a Line

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Open Ended

What do you wonder about today's topic?

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Slope of a Line

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Illustrating the Slope of a Line

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Review

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Illustrating the Slope of a Line

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Fill in the Blanks

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Type answer...

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Fill in the Blanks

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Type answer...

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Fill in the Blanks

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Type answer...

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Open Ended

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Did you find difficulty in describing the locations of the points?

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Open Ended

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Looking back at the graph, are points A and M vertically aligned?

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Open Ended

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What is the distance between points A and M?

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Open Ended

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Name all pairs of vertically aligned points and determine the distance

between the two vertically aligned points.

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Open Ended

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Are points A and I horizontally aligned?

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Open Ended

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What is the distance between points A and I?

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Open Ended

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Name all pairs of horizontally aligned points and determine the distance

between the two horizontally aligned points.

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Open Ended

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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

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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

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Situation 1: Teacher Carlo is travelling to two different hilly roads.

Which road is difficult to drive?

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Road 1

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Road 2

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Multiple Choice

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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?

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Road 3

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Road 4

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Open Ended

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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

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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)

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Illustrating the Slope of a Line

​m = rise / run

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Slope (m) - Road 1

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Illustrating the Slope of a Line

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Slope (m) - Road 2

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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

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Illustrating the Slope of a Line

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Slope (m) - Road 4

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Slope (m)

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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

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Illustrating the Slope of a Line

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Slope (m) - Road 5

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Slope (m)

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Illustrating the Slope of a Line

​The slope in road 6 is undefined.

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Multiple Choice

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Given the graph, what is the slope of the line?

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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

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​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

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​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

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​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

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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

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​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

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​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.

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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.

Solution: −𝐴 /𝐵 = −4 /−1 = 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

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?

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​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?

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​Finding the Slope of a Line Given an Equation

Mathematics 8

Illustrating the Slope of a Line

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​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

  1. I can describe the slope of a line;​

  2. I can determine the slope of a line given two points, an equation, and a

    graph; and

  3. ​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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