I UK 8TKA /'-/// //.VJP 87 



56i normal form of equation of straight line : second method 



il.l INMI- in iiiiii'l ih.it to get the 



r i- lion merely to obtain an equation that U satisfied 



iinate* of every point on the curve, and not 



satisfied l>\ tin- r...r. h natea of any >tlin j.-mt , ,ui<l that it 



U wholly miniatrrial what jiartinilar & v he 



ma}' in thf arroniplishiiu-iil nf this puriMi**. Thin 



is alreuds illustrated in Ai .here equation [10] 



unr.l in two ways, while Ex. ". p. 84, gives still a 



thinl nifth.Ml i.\ \\hi.-h the same equation may be f"tinl. 



So also it is possible to derive equation [13] by other 



fin ployed in Art. ~>4.* 

 1 draw a perpendicular from to the line 

 .!i -th U denoted by /?, and let a be the angle 

 \\lu.-li it makes with the s-uxis, then 



a ooe = />, and b sin = />, 



ut in-^ tlirsf valut-s !" <i and 6 in f.jiiati>n [10], it 

 , i.e. 



cos a sin a 



\\hirh is thf form already derived in Art. 54. 



*taiit. variaMes, etc., were illustrated by means 



of a triangle. Now that the ttudeut ha learned that the equation 

 - 1. for example, repreeeuU a straight line, U., that this equation 



is satisfied by all those pairs of rallies of z and y which are the coordi- 

 nate me, a somewhat betu-r illustration can be K 



Both x and y are variables, but are not independent ; each b an implicit 

 >tli<r. For any particular line a and 6 are constanU. l>ut 

 may represent other constants in the equation of another lin 

 H - arbitrary constants, and are often called parameters of the line. 



See also Ex. below. 



