What is the equation of the line that is parallel to the x-axis and passes through the point \((4,\,-3)\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(y=-3\)
A line parallel to the x-axis is horizontal, so every point on it has the same y-coordinate, and its equation is \(y=\) that value.
The line passes through \((4,\,-3)\), whose y-coordinate is \(-3\)
So every point of the line has \(y=-3\), and the equation is \(y=-3\)
Why the other options are incorrect
Option (1) \(x=4\) — Incorrect. This line passes through \((4,\,-3)\) but is parallel to the y-axis.
Option (3) \(x=-3\) — Incorrect. This is a vertical line through \((-3,\,0)\); it does not pass through \((4,\,-3)\).
Option (4) \(y=4\) — Incorrect. This is a horizontal line 4 units above the x-axis; it does not pass through \((4,\,-3)\).