H ;,: j 



TUK 8THAIGIH 



[li'j.aml [ I: | ( MI, a, and /M "Kent meanings) 



are trm- ..nl\ \\ hm the axes are rectangular. It may also be 



<-,! nut tiii- -ition, equa- 



\\ii.-n thr line is parallel to either 



jl"j :> inapplicable \vi lino pssSQS 



:in ; and equiitions [11] ami [1-] an- nut 



apph. .il.lo when the line is parallel to the y-axis. 



57. Every equation of the first degree between two variables 



has for its locus a straight line. It will probably not have 



escaped the rva that the five " standard " equa- 



i (filiations [9] to [13]) of the straight line, which have 



been derived in Arts. 51 to 54, are each of the first degree. 



lie shown that every equation of the first degree 



between two variables has a straight Hm- f<>r ito locus. The 



most general equation o .iml may be written in the 



Ax + Bu + C = 0, (I) 



\ / 



\\h'iv .1. //.and arc constants! ami neither .1 EMM />' :s 



Let P|a(*i< ^i) A^C 2 ^ y*)* and ^s^C^r y) ^ "f 



points on the locus of equation (1). Draw the ordi- 



Jby> r and M 9 P 9 ; also draw EP % and KP t 



parallel to the r-axis. 

 Then, by Art. 85(1), 





C=0.. 

 (7=0. ..(3) 



ther A or B. say A, to zero, then the equation may be written In the 

 i y which U the equation of a straight line parallel 



at the distance - from it [cf. Art. 38, 



B 



