1, let p,with coorinates (p,q), be a fixed point on the 'curve ' with equation y=mx+c and let Q with coordinates (r,s), be any other point on y=mx+c . use the fact thar the coordinates of p and Q satisfy the equation y=mx+c to show that the gradient of PQ is m for all positions of Q.
2 there are some values of a, b and c for which the equation ax+by+c=0 does not represent a straight line. give an example of such values
1)
3two lines have equations y=m1x+c1 and y=m2x+c2 and m1m2=-1. prove that the lines are perpendicular.
(p,q) on y=mx+c so q=mp+c (1)
(r,s) on y=mx+c so s=mr+c (2)
(1)-(2) gives q-s=m(p-r) so m=(q-s)/(p-r)
2) a=b=c=0. Any value of x and y satisfies the equation so the while x,y plane is the solution
