CHAPTER XXV 



215. The Straight Line Law. 

 Y 



FIG. 145. 



X 



Let PQ (Fig. 145) be any straight line, Q being the point where 

 this line cuts the axis of y ; let OQ = c, when c is positive this 

 point is above the origin and when c is negative the point Q is 

 below the origin. 



Let be the inclination of the line to the axis of x, the slope of 

 the line is therefore tan 6 ; let this be denoted by m. 



If P is any point on the line, its co-ordinates being (x, y] ; then 

 by drawing PR parallel to the axis of y, and QR parallel to the 

 axis of x, the right-angled triangle PQR is produced. 



Then 



or 



Hence 



PR 

 QR 



y-c 



= tan 



= m 



y = mx + c. 



This is the general equation of a straight line, and m and c are 

 constants for any particular straight line. A straight line will be 

 completely determined if the numerical values of m and c are 

 found. 



In dealing with questions on the straight line law, it is well to 

 give to the quantities x and y their most general meaning, x re- 



446 



