Question

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 = 1 )

b. ( y = 1 )

c. ( x = 4 )

d. ( y = 4 )

Explanation:

Step1: Recall properties of horizontal lines

A line parallel to the \(x\)-axis is a horizontal line. The equation of a horizontal line is of the form \(y = k\), where \(k\) is a constant (this is because for all points on the line, the \(y\)-coordinate is the same, and the \(x\)-coordinate can vary).

Step2: Determine the value of \(k\)

The line passes through the point \((1, 4)\). For a horizontal line \(y = k\), the \(y\)-coordinate of any point on the line is \(k\). Since the point \((1, 4)\) is on the line, the \(y\)-coordinate here is \(4\), so \(k = 4\). Thus, the equation of the line is \(y = 4\).

Answer:

D. \(y = 4\)