A simple example : $Z=3x_1 + 2x_2$
Z is a constant with no given value.
- $x_1, x_2 >0 $
- $ x_1 \leq 5$
- $ x_2 \leq 8$
The lecturer said that the slope is $-3/2$ , which I understand. However, he stated that all lines possible using that equation are parallel to the line passing through $(0,3)$ and $(2,0)$ . I want to know how did he deduce that assumption ? I tried giving $x_1$ and $x_2$ a value of zero and solve, however $Z$ has no given value. How did he know that the line would pass through $(0,3)$ and $(2,0)$ ?