The point P has coordinates (1,2) and the point Q has coordinates (A,B). A line parallel to PQ has the equation: -4x+3y=5 . Find an expression for A in terms of B

The initial step step is to determine the value for the gradient of the line PQ by analysing the gradient of the parallel line given. Since the line is parallel its gradient is equal to that of the line PQ and so, after rearranging the equation into the form y=mx+c, we can deduce that the gradient of the line PQ: m=4/3.The second step is to equate the equation of the gradient of a line ((y2-y1)/(x2-x1)) to the gradient determined above where the values (x2,y2) are equal to the point Q(A,B). Upon simplifying we find that A=3/4B-1/2