Question 876244
1	y  	=	2    	x	+	3	
Divide by	1						
	y  	=	2    	x	+	3    	
Compare this equation with y=mx+b							
slope m =	2    						
The slope of a line parallel to the above line will be the same							
The slope of the required line will be			2    				
m=	2    	,point	(	-4      	,	1	)
Find b by plugging the values of m & the point in							
y=mx+b							
1	=	-8      	+	b			
b=	9						
m=	2    						
Plug value of  the slope  and b					in y = mx +b		
The required equation is y  	=	2    	x	+	9      
		


x1	y1	x2	y2									
-4      	2    	1    	-1    									
												
The general equation of the line when co-ordinates of two points are given is												
												
{{{(y-	y1)/(	y1-y2) = (x-x1)/(x1-x2)}}}										
												
{{{(y-	2    	)/(	2    	-	-1    	)=(x-	-4      	)/(	-4    	-	1    	)}}}
												
												
{{{(y	-2      	)/(	3      	)=(x	+4      	) /(	-5      	)}}}				
												
{{{ 	-5      	(y+	-2      	) =	3      	(x-	-4      	)}}}				
												
-5      	y+	10      	=	3      	x+	12      						
												
-5      	y=	3      	x	2      								
/	-5      											
      	y=	-  3/ 5	x+	-  2/ 5								
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1	y  	=	2      	x	+	3    				
Divide by	1									
	y  	=	2      	x	+	3    				
Compare this equation with y=mx+b,					m= slope & b= y intercept					
slope m =	2    									
										
The slope of a line perpendicular to the above line will be the negative reciprocal										- 1/2
Because m1*m2 =-1										
The slope of the required line will be			- 1/2							
										
m=	- 1/2	,point	(	3	,	4	)			
Find b by plugging the values of m & the point in										
y=mx+b										
4	=	-3/ 2	+	b						
b=	11/2									
m=	- 1/2									
The required equation is		y  	=	-  1/ 2	x	+	11/ 2			



					
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