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Find whether the lines #3y-4x=5# and #4y+6=3x# are parallel or perpendicular?

Answer 1

Lines are neither parallel nor they are perpendicular to each other.

Converting #3y-4x=5# to slope intercept form we get #y=4/3x+5/3#, hence its slope is #4/3#.

Now converting #4y+6=3x# to slope intercept form we get #y=3/4x-6/4#, hence its slope is #3/4#.

While slope of parallel lines is always equal, product of slopes of perpendicular lines is #-1#. As neither slopes are equal nor their product is #-1#, lines are neither parallel nor they are perpendicular to each other.

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Answer 2

Sadie Allen

To find whether the lines (3y - 4x = 5) and (4y + 6 = 3x) are parallel or perpendicular, we need to compare their slopes.

The first equation, (3y - 4x = 5), can be rearranged to slope-intercept form: (y = \frac{4}{3}x + \frac{5}{3}). The slope of this line is (\frac{4}{3}).

The second equation, (4y + 6 = 3x), can be rearranged to slope-intercept form: (y = \frac{3}{4}x - \frac{3}{2}). The slope of this line is (\frac{3}{4}).

Since the slopes are not equal and the product of their slopes is not -1, the lines (3y - 4x = 5) and (4y + 6 = 3x) are neither parallel nor perpendicular.

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Answer from HIX Tutor

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