Final answer:
After converting both equations to slope-intercept form, the slopes are identified as (1/3) and 3. Since these are not negative reciprocals of each other, the lines represented by the given equations are not perpendicular.
Step-by-step explanation:
To determine if two lines are perpendicular, we must find their slopes and see if they are negative reciprocals of each other. For the equations -3x – 9y = 2 and 9x – 3y = -6 we need to put them into slope-intercept form (y = mx + b), where 'm' is the slope and 'b' is the y-intercept.
For the first equation: -3x – 9y = 2
- Divide by -9 to isolate y: y = (3/9)x – 2/9
- Simplify the slope: y = (1/3)x – 2/9
For the second equation: 9x – 3y = -6
- Divide by -3 to isolate y: y = (9/3)x + 2
- Simplify the slope: y = 3x + 2
The slopes are (1/3) and 3. The product of these slopes is (1/3) * 3 = 1. Since the slopes are not negative reciprocals of each other, the lines are not perpendicular.