How to draw graph with transformed axis

When a graph is drawn on ( y + x ) axis and ( y - x) axis instead of original how to convert it into original Please help with a detailed approach ?

-
 Is this a homework problem? If so please tag it homework. – Kazark Jul 3 '12 at 17:33 No this is not a homework problem. – Arpit Bajpai Jul 4 '12 at 1:31 This appeared in an exam – Arpit Bajpai Jul 4 '12 at 1:31 I wonder why it has been downvoted then. +1 – Kazark Jul 4 '12 at 16:23

The $y+x$ axis is located at $+45^{\circ}$ from the $+x$ axis. So the $+x$ axis in your first picture is at $-45^{\circ}$. When you rotate the $+x$ axis by $+45^{\circ}$ everything moves with it, so you should rotate the picture by $45^{\circ}$ counterclockwise.

-
 Had the same graph being drawn on y/x and 1 /x axis then what will be your answer – Arpit Bajpai Jul 3 '12 at 16:33 @ArpitBajpai: y/x vs. 1/x is not a simple rotation. There is not a simple graphic transformation that will take one to the other. You can certainly take points from one and replot it, but I have no geometric intuition like the above. – Ross Millikan Jul 3 '12 at 16:37 How did you find out y + x axis is located at +45 from the x axis – Arpit Bajpai Jul 3 '12 at 16:42 @ArpitBajpai: To do it mathematically, you use a rotation matrix: en.wikipedia.org/wiki/Rotation_matrix Intuitively, the perpendicular to the $y+x$ axis is the line where $y+x=0$, which is the line $y=-x$. – Ross Millikan Jul 3 '12 at 16:58 I believe y + x is located at 135 from the x – Arpit Bajpai Jul 3 '12 at 17:01