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Determine whether the line is parallel, perpendicular, or neither: 4x + y = 0 and 5x - 8 = 2y.

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Final answer:

The lines are neither parallel nor perpendicular. They intersect at a point.

Step-by-step explanation:

To determine whether the lines are parallel, perpendicular, or neither, we need to compare their slopes.

For the equation 4x + y = 0, we can rewrite it in slope-intercept form y = mx + b, where m represents the slope. Rearranging the equation, we have y = -4x.

For the equation 5x - 8 = 2y, we can rewrite it as y = (5/2)x - 4, where again, m represents the slope. Comparing the two slopes, we see that the slope of the first equation is -4 and the slope of the second equation is 5/2. Since these slopes are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular. They intersect at a point.

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