To determine whether the point $(2, 1)$ lies on the line defined by the equation $4x - 2y = 3$, we can substitute $x = 2$ and $y = 1$ into the equation and check if the equation holds true.

Substituting: $4(2) - 2(1) = 3$ $8 - 2 = 3$ $6 \neq 3$

Since $6 \neq 3$, the point $(2, 1)$ does not lie on the line $4x - 2y = 3$.

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Here are some related questions you might explore:

1. How do you find the slope of the line $4x - 2y = 3$?
2. How can we rewrite the equation $4x - 2y = 3$ in slope-intercept form?
3. How do you determine the distance between a point and a line?
4. How can we find the intersection of two lines algebraically?
5. How do we determine if two lines are parallel or perpendicular?

Tip: Always substitute the coordinates of a point into the line's equation to check if it lies on the line.