In the diagram below,the equation of the line AB is 4x + 5y = 40, the equation of the line BC is, y=x/5 the line AC passes through the points (6, 0) and (0, 10).
(a) Find the equation of the line through AC.
(b) The point S (5, 4) lies on the line through AB.
Find the equation of the line through S which is parallel to AC.
(c) Another point T lies on the line through AB such that its x-intercept (10, 0) is the midpoint between S and T.
(i) Find the coordinates of the point T.
(ii) Show that the distance between S and T is 12.8 units.
(d) The region inside the triangle ABC, not including points on the boundary, is described by 4x+ 5y < 40 and two other inequalities.
Write down the other two inequalities
(e) Given that (p, q) is a point inside the triangle ABC and that p and q are both integers, write down
(i) the largest possible value of p.
(ii) the least possible value of p + q.
(iii) the largest possible value of 4p + 5q.