9: y=mx+c

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This diagram shows two lines, one y=x and the other having a slope lesser than y=x. Since this line is y=mx, then doubtless, as we have seen in other lesson, m has to be less than 1 like m=1/2 or m=0.3 or m=0.866 etc. 
​Also m has to be greater than 0, otherwise, the line will pass through Q2 & Q4 and will not pass through Q1 & Q3 as shown here.

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In this diagram the line has a higher slope than y=x and thus y=mx as shown will have m>1. Once you understand the greater than > and the lesser than < symbols, understanding mathematics becomes very easy since a lot of information can then be compresses into small symbols like here when we say m>1

Now see y=-x

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See that the line y=-mx is below y=-x thus m is fractional i.e. m is between 0 and 1
And y = -nx is above y=-x in Q3 and thus m has to be greater than 1. Hope this is quite clear by now. 

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The two lines cut the y-axis at two different points which gives the constant term in y = mx + c. 

If you understand how c>0 and k<0 from the diagram, you would have learnt to interpret inequality.



EXERCISE

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For each of the four diagrams in the picture, look at y = mx and determine which of the four alternatives given below the diagram accurately denotes the nature of m.