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 \( 4x - 2y = 3 \).

Would you like more details or further explanation on this?

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.

Check if the point (2,1) lies on the line defined by the equation 4x - 2y = 3. This problem involves substituting the coordinates into the linear equation and verifying if the point satisfies it. Suitable for students in Grades 6-8.

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