Final answer:
The slope of a line perpendicular to the given line is -3/2 and the slope of a line parallel to the given line is 2/3.
Step-by-step explanation:
The equation of the line given is 4x - 6y = -9. To find the slope of a line perpendicular to this line, we need to find the slope of the given line and then find the negative reciprocal of that slope. The slope of the given line can be found by rearranging the equation into slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept. In this case, the equation becomes y = (2/3)x + 3/2, so the slope is 2/3. The negative reciprocal of 2/3 is -3/2, so the slope of a line perpendicular to the given line is -3/2.
To find the slope of a line parallel to the given line, we can use the fact that parallel lines have the same slope. So the slope of a line parallel to the given line is also 2/3.