To determine the equation of a line that is parallel to the given line y = 3x + 6 and passes through the point (9, -32), we can use the fact that parallel lines have the same slope.
The given line has a slope of 3, which means any line parallel to it will also have a slope of 3.
Using the point-slope form of a linear equation, we can write the equation as follows:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Substituting the values, we have:
y - (-32) = 3(x - 9)
Simplifying the equation further:
y + 32 = 3x - 27
Now, we can rearrange the equation to get it in the standard form (y = mx + b), where b is the y-intercept:
y = 3x - 27 - 32
y = 3x - 59
Therefore, the equation of the line that passes through the point (9, -32) and is parallel to the line y = 3x + 6 is y = 3x - 59.