Question

which equation represents a line which is perpendicular to the y-axis? answer y = -6 x = -6 x = -y x = (1/2)y

Explanation:

Step1: Recall line perpendicular to y - axis

A line perpendicular to the y - 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 a horizontal line, the \(y\) - coordinate remains the same for all values of \(x\).

Step2: Analyze each option

• Option 1: \(y=-6\) is in the form \(y = k\) (where \(k=-6\)), so it is a horizontal line, which is perpendicular to the y - axis.
• Option 2: \(x = - 6\) is a vertical line (since the \(x\) - coordinate is constant for all \(y\)), and a vertical line is parallel to the y - axis, not perpendicular.
• Option 3: \(x=-y\) can be rewritten as \(y=-x\), which is a line with a slope of \(- 1\), not a horizontal line.
• Option 4: \(x=\frac{1}{2}y\) can be rewritten as \(y = 2x\), which is a line with a slope of \(2\), not a horizontal line.

Answer:

\(y = - 6\) (the first option)