A line with a slope of 0 is a horizontal line. This means it has the same y-coordinate for all values of x.
Since the line passes through the point (4, -6), the y-coordinate of the line will always be -6.
The slope-intercept form of a line is given by the equation:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept. Since the slope \( m \) is 0, the equation simplifies to:
\[ y = 0 \cdot x + b \] \[ y = b \]
Since the line passes through (4, -6), we know that the value of \( b \) is -6. Thus, the slope-intercept equation of the line is:
\[ y = -6 \]
This is the equation of the horizontal line that passes through the point (4, -6).