[Cn. II. 



tion in y or z only will represent planes parallel to the zx- or 

 j-y-pl 



Any algel'i / in one variable represents one or 



more planet parallel to a coordinate plane. 



It follows at once by Art. 39, that two Minultaneous 

 equations of the first degree in one variable represent the 

 intersection of two planes parallel to coordinate pi., 

 therefore, represent a straight line parallel to the co< 

 nate axis of the third variable ; e.g., y = b, z = c, considered 

 as simultaneous equations, represent a straight line parallel 

 to the x-axis. 



210. Equations in two variables. Cylinders perpendicular 

 to coordinate planes. Consider the equation 



J/+3y=6, (1) 



with two variables only. In the xy -plane it represents a 

 straight line AB. If, now, from any point P of AB a 



.149. 



straight line be drawn parallel to the z-axis, the x and // 



1 1 nates of every point Q on this line will be the same as 



for /'. and therefore satisfy equation (1). Moreover, if the 



line PQ moved along AB, and always parallel to the 2-axis, 



