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Are the two lines #15x-3y = 12# and #y = 5x + 7# parallel or perpendicular?

Answer 1

#15x-3y = 12# and be written as #color(white)("XXXXX")##y = 5x-4# which is a line with slope #5#

#y=5x+7# also has a slope of #5#

Therefore the two lines are parallel.

The above assumes recognition of the slope y-intercept form for a line: #color(white)("XXXXX")##y = mx +b# which has a slope of #m# and a y-intercept of #b#.

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Answer 2

Avery Alexander

To determine if the two lines are parallel or perpendicular, convert both equations to slope-intercept form (y = mx + b), and compare their slopes.

First equation: (15x - 3y = 12) [15x - 12 = 3y] [-3y = 15x - 12] [y = -5x + 4] The slope ((m)) of the first line is (-5).

Second equation is already in slope-intercept form: (y = 5x + 7). The slope ((m)) of the second line is (5).

Lines are parallel if their slopes are equal. Lines are perpendicular if their slopes are negative reciprocals of each other, meaning (m_1 \cdot m_2 = -1).

In this case, the slopes are (-5) and (5), which are not equal, and their product is (-5 \cdot 5 = -25), not (-1). Thus, the lines are neither parallel nor perpendicular.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.