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To determine if the line \( 4x + 3y - 16 = 0 \) passes through the point \( (4, 0) \), we need to substitute the coordinates of the point into the equation and see if it satisfies the equation.

Given:
- Line equation: \( 4x + 3y - 16 = 0 \)
- Point: \( (x, y) = (4, 0) \)

Substitute \( x = 4 \) and \( y = 0 \) into the equation:

\[
4(4) + 3(0) - 16 = 16 + 0 - 16 = 0
\]

Since the left-hand side equals the right-hand side, the equation is satisfied.

**Answer: Yes, the line passes through the point (4, 0).**

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the general method for determining if a point lies on a line given by an equation?
2. How do you find the slope of the line \( 4x + 3y - 16 = 0 \)?
3. Can a point not on the line have its coordinates substituted into the line equation?
4. How can you find the y-intercept of the line \( 4x + 3y - 16 = 0 \)?
5. What are the steps to convert the line equation \( 4x + 3y - 16 = 0 \) into slope-intercept form?

**Tip:** To check if a point lies on a line, always substitute the point's coordinates into the line equation and verify if the equation holds true.

Does the line 4x + 3y - 16 = 0 pass through the point (4,0)?

This problem tests whether the line 4x + 3y - 16 = 0 passes through the point (4,0). Using substitution of coordinates, we determine if the point satisfies the equation. A detailed solution is provided, suitable for Grades 6-8.

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