What is the equation of the line perpendicular to #y=-11/16x # that passes through # (3,7) #?

1 Answer
May 20, 2018

Answer:

#16x-11y=-29#

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"#

#y=-11/16x" is in this form with "m=-11/16,b=0#

#"given a line with slope m then the slope of a line"#
#"perpendicular to it is"#

#•color(white)(x)m_(color(red)"perpendicular")=-1/m#

#rArrm_("perpendicular")=-1/(-11/16)=16/11#

#rArry=16/11+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(3,7)" into the partial equation"#

#7=48/11+brArrb=77/11-48/11=29/11#

#rArry=16/11x+29/11larrcolor(red)"in slope-intercept form"#

#"multiply all terms by 11 and rearrange"#

#11y=16x+29#

#rArr16x-11y=-29larrcolor(red)"in standard form"#