School: a monthly record of educational thought and progress . FIG. 4 EDUCATIONAL THOUGHT AND PROGRESS 141. little time given to this subject when dealing with thestraight line would help to remove one of the mostserious difficulties in the way of students who havereached curves of the second or higher degree—,the geometrical interpretation of such an equation as (Ax + By + cf = k (Px + Qy + R)and the converse process. Simple cases like the func-tions X + y, X — y might come in from the first, andextensions made in the successive revision courses. Thesame investigation, so helpful in plott
School: a monthly record of educational thought and progress . FIG. 4 EDUCATIONAL THOUGHT AND PROGRESS 141. little time given to this subject when dealing with thestraight line would help to remove one of the mostserious difficulties in the way of students who havereached curves of the second or higher degree—,the geometrical interpretation of such an equation as (Ax + By + cf = k (Px + Qy + R)and the converse process. Simple cases like the func-tions X + y, X — y might come in from the first, andextensions made in the successive revision courses. Thesame investigation, so helpful in plotting a straight-linegraph and in distinguishing the positive and negativesides of a straight line, also helps to fix the geometricalinterpretation of Kx + By + C on the mind and todeduce the well-known formula connecting it with theexpression for the perpendicular from (x, y) to hx -j-By -f C = O. Thus : From the point P (x, y) letparaUels to OX, OY meet Kx -f By + C = O in H, K,and let PL be perpendicular to it. Then, since P is reached by the step HP from a pointH at which the function Kx -f By +
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