Question

which equation represents a line which is parallel to the y - axis?
answer
$x=-4y$
$y=x - 3$
$x=-8$
$y=-7$

Explanation:

Step1: Recall the properties of lines parallel to the y - axis

A line parallel to the y - axis has an equation of the form \(x = k\), where \(k\) is a constant. This is because for all points on the line, the \(x\) - coordinate is the same, and the \(y\) - coordinate can take any real value.

Step2: Analyze each option

• For the equation \(x=-4y\), we can rewrite it in slope - intercept form \(y =-\frac{1}{4}x\). This is a line with slope \(m =-\frac{1}{4}\), not parallel to the y - axis.
• For the equation \(y=x - 3\), it is in the slope - intercept form \(y=mx + b\) with slope \(m = 1\), not parallel to the y - axis.
• For the equation \(x=-8\), it is of the form \(x = k\) (where \(k=-8\)). So, this line is parallel to the y - axis.
• For the equation \(y=-7\), it is of the form \(y = k\) (where \(k =-7\)). This is a line parallel to the x - axis.

Answer:

\(x=-8\)