which of the following is the equation of a line that passes through the point (1,4) and is parallel to the x-axis A.x=4 B.x=1 C.y=1 D.y=4?

The x-axis (y = 0) is horizontal; it has 0 slope, and so will a line parallel to this. The only line that satisfies that condition and goes through (1, 4) is y = 4. The answer is D).

A) and B) can be dismissed immediately because both of those lines are vertical and have an undefined slope, making them both perpendicular.

D. y = 4

Parallel to x-axis means slope is 0.
y-4 = 0(x-1)
y = 4