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But in all ncert questions i have read so far it has been done like this:if a line ax+by>0 passing through origion then shade below line and vice versa

Asked by upmaniousagarika 26th May 2016, 11:19 PM
Answered by Expert
Answer:
begin mathsize 12px style I n space N C E R T space b o o k space i t space h a s space n o t space b e e n space d o n e space t h e space w a y space y o u space h a v e space m e n t i o n e d.
L e t space u s space t a k e space a n space e x a m p l e space a n d space s e e space f o r space o u r s e l v e s comma space w h i c h space r e g i o n space t o space s h a d e.
S u p p o s e comma space w e space h a v e space t o space f i n d space t h e space r e g i o n space x plus y greater than 0
S o space w e space d r a w space t h e space l i n e space x plus y equals 0 comma space a s space s h o w n space i n space t h e space f i g u r e. space end style
N o w comma space l o o k space a t space t w o space p o i n t s space i n space t h i s space X Y space p l a n e.
left parenthesis negative 2 comma space 0 right parenthesis space a n d space left parenthesis 0 comma space 4 right parenthesis
left parenthesis negative 2 comma space 0 right parenthesis space i s space b e l o w space t h e space s t r a i g h t space l i n e comma
w h e r e a s comma space left parenthesis 0 comma space 4 right parenthesis space i s space a b o v e space t h e space s t r a i g h t space l i n e.

F o r space left parenthesis negative 2 comma space 0 right parenthesis comma space x plus y equals negative 2 plus 0 equals negative 2 comma space w h i c h space i s space n e g a t i v e.
F o r space left parenthesis 0 comma space 4 right parenthesis comma space x plus y equals 0 plus 4 equals 4 comma space w h i c h space i s space p o s i t i v e.
S o comma space left parenthesis negative 2 comma space 0 right parenthesis comma space w h i c h space i s space b e l o w space t h e space s t r a i g h t space l i n e comma space i s space i n space t h e space r e g i o n
f o r space w h i c h space x plus y less than 0
S i m i l a r l y comma space left parenthesis 0 comma space 4 right parenthesis comma space w h i c h space i s space a b o v e space t h e space s t r a i g h t space l i n e comma space i s space i n space t h e space r e g i o n
f o r space w h i c h space x plus y greater than 0
S o space t h e space r e g i o n space x plus y greater than 0 space i s space a s space s h o w n space b e l o w.
 
In general, given any linear equation ax+by+c > or < 0,
first write the inequality in the form y > or < other terms, by taking all other terms to right hand side.
Finally, if you get an inequality of form y > (some expression), then shade the region above the line.
If you get an inequality of the form y < (some expression), then shade the region below the line
Answered by Expert 29th May 2016, 5:30 PM
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