Graph the equation. Let x equals negative 3 comma negative 2 comma negative 1 comma ​0, 1,​ 2, and 3.
y equals negative 4

To graph the equation \( y = -4 \) for the given values of \( x \) \((-3, -2, -1, 0, 1, 2, 3)\), follow these steps:

1. Recognize that \( y = -4 \) is a horizontal line where the \( y \)-value is always -4, regardless of the \( x \)-value.

2. Plot the points for the given \( x \)-values with \( y = -4 \):
   - For \( x = -3 \), \( y = -4 \)
   - For \( x = -2 \), \( y = -4 \)
   - For \( x = -1 \), \( y = -4 \)
   - For \( x = 0 \), \( y = -4 \)
   - For \( x = 1 \), \( y = -4 \)
   - For \( x = 2 \), \( y = -4 \)
   - For \( x = 3 \), \( y = -4 \)

3. Draw a horizontal line passing through all these points on the coordinate plane.

Here is the graph:

\[
\begin{array}{ccccc}
  x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
  y & -4 & -4 & -4 & -4 & -4 & -4 & -4 \\
\end{array}
\]

Now let's visualize this on a coordinate plane:

\[
\begin{tikzpicture}
\begin{axis}[
    axis lines = middle,
    xlabel = \(x\),
    ylabel = \(y\),
    ymin = -5, ymax = -3,
    xmin = -4, xmax = 4,
    xtick={-3, -2, -1, 0, 1, 2, 3},
    ytick={-4},
    grid = major,
    width=10cm, height=6cm
]

\addplot[
    color=blue,
    mark=*,
    only marks,
    domain=-3:3
]
{-4};

\addplot[
    color=blue,
    samples=100,
    domain=-3:3
]
{-4};

\end{axis}
\end{tikzpicture}
\]

### Would you like more details or have any questions?

### Further Exploration Questions:

1. How would the graph look if the equation were \( y = 4 \) instead?
2. What is the slope of the line \( y = -4 \)?
3. How can we express the horizontal line equation in slope-intercept form?
4. What is the y-intercept of the line \( y = -4 \)?
5. How does the line \( y = -4 \) compare to the line \( x = -4 \)?
6. If you shift the line \( y = -4 \) up by 5 units, what will the new equation be?
7. What will be the coordinates of the points if \( x \) ranges from -5 to 5 for the equation \( y = -4 \)?
8. How would the graph change if the equation were \( y = -4 + x \)?

### Tip:
When graphing horizontal lines, remember that the y-value remains constant across all x-values.

Learn how to graph the equation y = -4 for the values of x = -3, -2, -1, 0, 1, 2, 3. This problem covers graphing horizontal lines on a coordinate plane. Suitable for students in Grades 6-8.

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