What is the equation of a line that passes through the point (-1, -9) and has a slope of zero?

Understand the Problem

The question is asking for the equation of a line that has a slope of zero and passes through the point (-1, -9). This indicates that the line is horizontal.

Answer

$y = -9$

Steps to Solve

Identifying the properties of the line

Since the slope is zero, this indicates that the line is horizontal. A horizontal line passing through any point will have the same $y$-value for all $x$.

Using the point to write the equation

The point given is (-1, -9). Since the $y$-value of the point is -9, the equation of the line will be:

$$ y = -9 $$

This means that for any value of $x$, $y$ will always equal -9.

Understanding the options

Now, we must determine which option matches our equation.

The options are:

$x = -9$ (not a horizontal line)
$y = -9$ (matches our line)
$x = -1$ (not a horizontal line)
$y = -1$ (not a match)

The equation of the line is $y = -9$.

More Information

A horizontal line has a constant $y$-value regardless of $x$. This means that if the slope is zero, it can be described using the $y$-coordinate of any point it passes through.

Tips

Confusing horizontal lines with vertical lines. Remember, horizontal lines have a constant $y$ value, while vertical lines have a constant $x$ value.

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