The linear equation is: y=kx-2k+3.

Requirements: The triangle has the largest area.

You can make x=0 and get y = 3-2k；;

Let y=0 and x = 2-3/k.

Then, find the triangle area;

S=x*y/2=(3-2k)*(2-3/k)/2

All that remains is to find the maximum.

The solution is k=-3/2.

That is, the linear equation is: y=-3x/2+6.