# Are these two lines parallel, perpendicular, or neither? Explain. #9x+3y=8#, #3x+9y=8#

The given lines are neither parallel nor perpendicular.

The first line is:

The second line is:

From those equations we can see that those lines are neither parallel nor perpendicular

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To determine if two lines are parallel, perpendicular, or neither, we examine their slopes. We first rewrite the equations in slope-intercept form (y = mx + b), where m represents the slope:

For the first equation, 9x + 3y = 8: [3y = -9x + 8] [y = -3x + \frac{8}{3}]

For the second equation, 3x + 9y = 8: [9y = -3x + 8] [y = -\frac{1}{3}x + \frac{8}{9}]

Comparing the slopes of the two lines:

The slope of the first line is -3. The slope of the second line is -1/3.

Since the product of the slopes is not -1, the lines are not perpendicular. Since the slopes are not equal, the lines are not parallel. Therefore, these lines are neither parallel nor perpendicular.

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