What is the equation of the line that is parallel to the x-axis and passes through the point \((-5,\,8)\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(y=8\)
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 \((-5,\,8)\), whose y-coordinate is \(8\)
So every point of the line has \(y=8\), and the equation is \(y=8\)
Why the other options are incorrect
Option (1) \(x=-5\) — Incorrect. This line passes through \((-5,\,8)\) but is parallel to the y-axis.
Option (3) \(x=8\) — Incorrect. This is a vertical line through \((8,\,0)\); it does not pass through \((-5,\,8)\).
Option (4) \(y=-5\) — Incorrect. This is a horizontal line 5 units below the x-axis; it does not pass through \((-5,\,8)\).