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From Karnataka Open Educational Resources
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Line 27: + + + + − + − Line 46:
Line 49: − + − − Ask the students to observe the given table describe the pattern using words .<br>Ask them to plot and join the points on grids and ask how the line segments is visible in the graph. <br> ask them to write the relation between X and Y.<br>(we can come to a conclusion that the larger the absolute value of the number,the linebecomes steeper.) − {|Class="wikitable" − |- − |X − |Y − |- − |6 − |1 − |- − |7 − |2 − |- − |8 − |3 − |- − |9 − |4 − |} − {|Class="wikitable" − |- − |X − |Y − |- − |4 − |1 − |- − |5 − |3 − |- − |6 − |5 − |} − {|Class="wikitable" − |- − |X − |Y − |- − |6 − |1 − |- − |7 − |4 − |- − |8 − |7 − |- − |} − [[File:Slope of segment.png|250px]]<br> − + − #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?<br> − 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.<br> − 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? − [[Image:Measure of Slope.png|250px]] − #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? − − ==Concept 2== − Line 119:
Line 58: − + + − + − The following Geogebra applet helps in visualising Positive and negetive Slope − + − <ggb_applet width="1368" height="551" version="4.2" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />+ − <br> − ==Concept 3==<br> − Slopes of Parallel and Perpendicular lines Line 135:
Line 71: + + +
added Category:Co-ordinate Geometry using HotCat
=Additional Information=
=Additional Information=
==Useful websites==
==Useful websites==
[http://www.virtualnerd.com/algebra-1/linear-equation-analysis/slope-rate-of-change/understanding-slope/negative-slope-definition For more video lessons on Slope click]<br>
[http://projects.cbe.ab.ca/Aberhart/jkotow/interactives/interactives.htm For playing with Geogebra applets online click]
==Reference Books==
==Reference Books==
= Teaching Outlines =
= Teaching Outlines =
==Concept 1==
=='''understanding what is a Slope'''==
'''understanding what is a Slope'''
===Learning objectives===
===Learning objectives===
#Slope is measure of the steepness of a line.
#Slope is measure of the steepness of a line.
===Activities===
===Activities===
#Activity No1<br> '''understanding What is a slope? '''
#Activity No #1 '''[[understanding what is Slope of a line]]'''
'''Procedure'''<br>
=='''Assessment Questions'''==
=='''Positive and Negetive Slope'''==
'''Positive and Negetive Slope'''
===Learning objectives===
===Learning objectives===
#Students should also be able to visualise a line with positive and negetive Slope
#Students should also be able to visualise a line with positive and negetive Slope
===Notes for teachers===
===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 decreases corresponding line will have Negetive Slope
If the change in Y with the value of X increases corresponding line will have Positive Slope
If the change in Y with the value of X increases corresponding line will have Positive Slope<br>
===Activities===
===Activities===
#Activity No #1 <br>
#Activity No 1[[ Positive and negetive slope]]<br>
=Geogebra Applet=
=='''Slopes of Parallel and perpendicular lines'''==
#Activity1 [[Slope of parallel and perpendicular lines]]
= Hints for difficult problems =
= Hints for difficult problems =
= Math Fun =
= Math Fun =
[[http://karnatakaeducation.org.in/KOER/en/index.php/Co-ordinate_geometry Back to Co-ordinategeometry Topic page]]
[[Category:Co-ordinate Geometry]]
