How do you tell whether the lines for each pair of equations are parallel, perpendicular, or neither: #y=-4x+3, -2x+8y=5#?

1 Answer
May 3, 2018

Answer:

#"lines are perpendicular"#

Explanation:

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#"express both equations in this form and consider their"#
#"slopes"#

#• " parallel lines have equal slopes"#

#• " the product of the slopes of perpendicular lines equals -1"#

#y=-4x+3larrcolor(blue)"is in slope-intercept form"#

#"with slope m "=-4#

#"rearranging "-2x+8y=5larrcolor(blue)"add 2x to both sides"#

#rArr8y=2x+5#

#"divide all terms by 8"#

#rArry=1/4x+5/8larrcolor(blue)"in slope-intercept form"#

#"with slope "=1/4#

#-4!=1/4" hence lines are not parallel"#

#-4xx1/4=-1" hence lines are perpendicular"#