Question

question
which equation represents a line which is parallel to the x-axis?

answer
○ ( x = \frac{1}{2}y ) ○ ( x = 5 )
○ ( y = -1 ) ○ ( y = x )

Explanation:

Step1: Recall the slope of x - axis

The x - axis is a horizontal line, and its slope \(m = 0\). A line parallel to the x - axis is also a horizontal line, and the equation of a horizontal line is of the form \(y=k\), where \(k\) is a constant. This is because for a horizontal line, the \(y\) - coordinate of all points on the line is the same, and the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=0\) (since \(y_2 - y_1 = 0\) for any two points on the line).

Step2: Analyze each option

• Option \(x=\frac{1}{2}y\) (or \(y = 2x\)): This is a linear equation with slope \(m = 2\), which is a non - horizontal line (it has a positive slope), so it is not parallel to the x - axis.
• Option \(x = 5\): This is a vertical line (the equation of a vertical line is \(x = k\), where \(k\) is a constant). The slope of a vertical line is undefined, and it is parallel to the y - axis, not the x - axis.
• Option \(y=-1\): This is in the form \(y = k\) (where \(k=-1\)), so it is a horizontal line with slope \(m = 0\), which means it is parallel to the x - axis.
• Option \(y = x\): This is a linear equation with slope \(m = 1\), which is a non - horizontal line (it has a positive slope), so it is not parallel to the x - axis.

Answer:

\(y=-1\) (the option with \(y = - 1\))