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
$y = -9$
Answer for screen readers
The equation of the line is $y = -9$.
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.
