Any line is completely determined by two points.
I.e., One and only one line can intersect two points (in Euclidean, Cartesian plane).
So it suffices to find two points on a given line.
Note: you can discover two points easily by setting $\quad x_1 = 0\implies x_2 =\dfrac Z2\quad$ and setting $\quad x_2 = 0 \implies x_1 = \dfrac Z3,\quad$ thus giving you the two points you need to graph the line!
Using your example, we can learn more about the line, and find an expression which plots one variable as a function of the other: $Z=3x_1 + 2x_2,$ with $Z$ is some constant (a particular value, depending on context). (You mention "plotting a line", so I am assuming we have a strict line.)
$\text{Let}\quad y = x_1, x = x_2\quad$ (so we can plot the function of one variable in terms of the other. You can use a same procedure, as what follows, if you want to plot $y = x_2$ in terms of $x = x_1$.)
$Z = 3y + 2x \iff -3y = 2x - Z \iff y = -\dfrac 23x + \dfrac Z3\quad \left(x_1 = -\dfrac 23 x_2 + \frac Z3\right)$
Then you have the equation for the line in slope-intercept form:
The line intersects the y-axis at $x = 0 \implies y = \dfrac{Z}{3}$, so one point is $\left(0, \frac{Z}{3}\right).$ (This is called the y-intercept). Then use "slope" $m$, which is the coefficient of the $x$ term, here $m = -\dfrac23 = \dfrac{\text{rise}}{\text{run}}$.
Slope will given you information about how one variable relates to the other. Positive slope givens you a line where one variable correlates positively with the other; negative slope gives you a line where one variable correlates negatively with the other variable.
From the y-intercept, move down two units (i.e., $-2$) along the y-axis, and three units in the positive x-direction, to the point $\left(3, \frac Z3 - 2\right)$.
With two points on the line (two points satisfying the equation), you can use a straightedge to draw the line connecting/intersecting the points and thereby plot the given line.