A student was asked to draw the graph of the line 2x+3y−6=0. She marked the points P(0,3) and Q(2,0), joined them, and claimed that the drawn line represented the required equation.
(i) Determine the correct x–intercept and y–intercept of the given equation directly from the equation itself.
(ii) Compare the student’s chosen points P and Q with the correct intercepts and explain, using coordinates, why her choice is incorrect.
(iii) Describe how plotting the incorrect points would shift the position of the line on the graph paper. Indicate the direction in which the incorrect line would be displaced relative to the correct one.
(iv) Redraw, on your answer sheet, a small labelled sketch (no scale required) showing both the student’s incorrect line and the correct line to illustrate the error.