Difference between revisions of "Slope of a line"
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The following Geogebra applet helps in visualising Positive and negetive Slope | The following Geogebra applet helps in visualising Positive and negetive Slope | ||
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<ggb_applet width="1368" height="551" version="4.2" 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Revision as of 19:50, 13 August 2014
| Philosophy of Mathematics |
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Concept Map
Textbook
Please click here for Karnataka and other text books.
Additional Information
Useful websites
For more video lessons on Slope click
Reference Books
Teaching Outlines
understanding what is a Slope
Learning objectives
- Slope is measure of the steepness of a line.
- Students will understands that slope increases with the steepness.
- Students will recognize and make a connection between the magnitude of the slope and the steepness of a line.
- Students will understands that Slope is a number (magnitude).
- Students understands that Slope is the orientation or inclination of a line with the X-axis.
- Students should also be able to draw a line with a specific slope.
Notes for teachers
Slope is a number which represents the steepness of a line Students can relate the slope of line to the tangent of the angle of elevation.
Activities
- Activity No1
understanding What is a slope?
Procedure
Ask the students to observe the given table describe the pattern using words .
Ask them to plot and join the points on grids and ask how the line segments is visible in the graph.
ask them to write the relation between X and Y.
(we can come to a conclusion that the larger the absolute value of the number,the linebecomes steeper.)
| X | Y |
| 6 | 1 |
| 7 | 2 |
| 8 | 3 |
| 9 | 4 |
| X | Y |
| 4 | 1 |
| 5 | 3 |
| 6 | 5 |
| X | Y |
| 6 | 1 |
| 7 | 4 |
| 8 | 7 |
Assessment Questions
- Write the relation between X and Y(as an equation)
- plot the other points following the same pattern and join the points
- How do we differentiate these lines from one another?from the inclination with the x-axis i.e bending of line towards x-axis
- Can we visualise the angle so formed by the line with the X-axis?
- What is the relation between the bending of line and angle formed by it with the X-axis?
We can conclude that bending(orientation of line)increases with the increse in the angle or we can say line becomes steeper with the angle of inclination.
The slope of a line is a number that measures its "steepness" It is the change in y for a unit change in x along the line.
- How do we measure the steepness of line?
- Ask the students to measure Slope of other lines
- Ask the students to inspect the Slope with the help of relation between X and Y
- What is the slope of a horizontal and a Vertical line?
- Find the slope of three segments of the triangle given below.
Positive and Negetive Slope
Learning objectives
- Students should also be able to visualise a line with positive and negetive Slope
- Students should also be able to differentiate a line with positive and negetive Slope
Notes for teachers
If the change in Y with the value of X decreases corresponding line will have Negetive Slope
If the change in Y with the value of X increases corresponding line will have Positive Slope
Activities
- Activity No 1
Observe the following table and analyse the relation between X and Y (X,Y).
You will find that in one case the value of Y goes on incresing with the value of x ,but in the other case the value of Y goes on decreasing with the value of x.
In both the cases visualise the orientation of line segment.
If the value of Y decrease with the value of X the line will have negetive slope
If the value of Y increse with the value of X the line will have negetive slope
- Activity No 2
The following Geogebra applet helps in visualising Positive and negetive Slope