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matrixmystics.md

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 1. Ram and Lakshman were two brothers, Ram's pocket money was twice as much as Lakshman. The good boy that Ram and Lakshman were, they did not spend their pocket money on anything. They instead saved the same in their piggy bank. Every week, they would check their savings so far. Assume the first week's savings was $$(R_1,L_1)$$ and second week's $$(R_2,L_2)$$ and so on. They try plotting their weekly savings on a graph sheet. How will the points look like?
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 2. Atul's house is centered at origin $$(0,0)$$ he walks straight (along the x-axis) for 2 units and then takes a left and walks 1 unit to reach Bala's house, after that he takes a right turn and walks for one unit and then a left turn and walks for one unit and reaches Chetan's house. He continues in a similar style, takes a right turn 1 unit and then left turn one unit and reaches Divya's house. Are the houses of Bala, Chetan and Divya on a straight line? What is the equation of this line? Plot this on Geogebra  
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 3. Plot the lines $$y=x$$, $$y=2x$$, $$y=10x$$.  
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 4. Observe that they all pass through the origin. Why?  
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 5. Plot $$y=2x+1$$. Observe, Why doesn't it pass through the origin?
 
 6. Plot $$y=ax+b$$, with $$a$$ and $$b$$ as parameters which you should be able to vary. What do you observe?