To determine the equation of the line passing through the points \((-4, 9)\) and \((-1, 9)\), we first observe that both points have the same \(y\)-coordinate (9). This indicates that the line is horizontal.
For a horizontal line, the equation can be expressed as:
\[ y = c \]
where \(c\) is the \(y\)-coordinate for all points on the line. Since both points have a \(y\)-coordinate of 9, the equation of the line is:
\[ y = 9 \]
If the question specifically asks for the point-slope form, a horizontal line can also be expressed using the slope and one of the points. The slope \(m\) of a horizontal line is \(0\). The point-slope form is given by:
\[ y - y_1 = m(x - x_1) \]
Using the point \((-4, 9)\) and the slope \(m = 0\):
\[ y - 9 = 0(x + 4) \]
Simplifying this gives:
\[ y - 9 = 0 \]
which simplifies to:
\[ y = 9 \]
In conclusion, the equation of the line in fully simplified point-slope form is:
\[ y = 9 \]
or in point-slope form using one of the points:
\[ y - 9 = 0(x + 4) \]
Both forms express the same horizontal line.