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Use slopes to determine if the lines - 3x – 9y = 2 and 9x – 3y = -6 are perpendicular.

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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.

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