Answer:
the line equation is 2*x - y = 3
Step-by-step explanation:
for the line equation in implicit form
A*x + B*y = C
then if the point (x=4,y=5) belong to the line
4*A + 5*B = C
and if the point (x=7,y=11) belong to the line
7*A + 11*B = C
then since we can choose C freely , we set C=1 for simplicity , then
4*A + 5*B = 1 → B= (1-4*A)/5
7*A + 11*B = 1
7*A + 11*(1-4*A)/5 = 1
7*A - 44/5*A + 11/5 = 1
-9/5*A = -6/5
A= 2/3
B= (1-4*A)/5 = (1-4*2/3)/5 = -1/3
therefore
2/3*x - 1/3*y = 1
2*x - y = 3
