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 has 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 in the form \(y=mx + b\) with \(m = 2\), which is a line with a non - zero slope (slope \(2\)), 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, so it is not parallel to the x - axis (a horizontal line).
• Option \(y=-1\): This is in the form \(y = k\) (where \(k=-1\)), which is a horizontal line. The slope of this line is \(0\), so it is parallel to the x - axis.
• Option \(y = x\): This is a linear equation in the form \(y=mx + b\) with \(m = 1\), which is a line with a non - zero slope (slope \(1\)), so it is not parallel to the x - axis.

Answer:

\(y=-1\)