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  1. Determine an equation for a line that is perpendicular to Â«math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»6«/mn»«/math» and has a y-intercept of –3.

    The slope of the original line is 5. The negative reciprocal of 5 is Â«math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»-«/mo»«mfrac mathcolor=¨#B94A48¨»«mn»1«/mn»«mn»5«/mn»«/mfrac»«/math», so the slope of the new line is Â«math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»-«/mo»«mfrac mathcolor=¨#B94A48¨»«mn»1«/mn»«mn»5«/mn»«/mfrac»«/math». The y-intercept is –3, so there is enough information to write an equation in slope-intercept form.



  2. Two lines have slopes of –0.2 and 4. Are the two lines perpendicular?

    If the two lines are perpendicular, their slopes will have a product of –1.

    −0.2(4) = −0.8

    The two lines are not perpendicular.