[Graphs and Relations] Sliding technique

[Daenerys Targaryen]

So I'm going through some exam solutions and I see something called the 'sliding line technique', I've never heard nor learnt this before, and yet it seems to be an easier way of getting the max/min objective figure.

Anyone care to explain how to do it?

Thanks.

[Stick]

Case I: Z=ax+by, Z=-ax+by
1. Let Z equal any number (a common multiple of a and b is ideal).
2. Draw the objective function onto the graph.
3. Position your ruler so it is parallel with the line and slide it from the bottom of the graph to the top of the graph. The first point crossed is the minimum and the last point crossed is the maximum.

Case II: Z=ax-by, Z=-ax-by
1. Let Z equal any number (a common multiple of a and b is ideal).
2. Draw the objective function onto the graph.
3. Position your ruler so it is parallel with the line and slide it from the top of the graph to the bottom of the graph. The first point crossed is the minimum and the last point crossed is the maximum.

[Daenerys Targaryen]

Oh nice explanation. Clear and concise.
Does it work 100% with all of these kinda questions?

[Stick]

Yes, but it might not work too well if the points are very close together. And, of course, this method does not give you the value of the maximum - it only locates it for you.

[Daenerys Targaryen]

Aha yeah. Thanks dude.