Every square gets one diagonal line, either \ or /. Numbers sit on the corners where squares meet, and each one tells you how many of the lines around it touch that corner.
A 0 means every line around it points away; a 4 means they all point in. Edge and corner numbers are especially helpful because fewer squares touch them.
The final rule ties it together: the lines may never join up into a closed loop. When a line would complete a loop, it has to slant the other way.
Draw \ or / in every square so that each corner number counts the lines touching it, with no closed loops.
The full guide, with a worked example and common mistakes: How to play Slant Lines.
A \ touches the top-left and bottom-right corners of its square; a / touches the top-right and bottom-left.
Yes — the puzzle is solved only when every square has a line.
Yes — every puzzle is checked so that logic alone reaches the answer.