What is the equation of the line perpendicular to #y=-7/16x # that passes through # (5,4) #?

2 Answers
Mar 13, 2018

Answer:

#y=16/7x-52/7#

See details below

Explanation:

If a line has the equation #y=mx#, we call slope to #m# and whatever perpendicular line to it has then the equation #y=-1/mx#

In our case #y=-7/16x#, then, the slope is #m=-7/16#, so the perpendicular has slope #m´=-1/(-7/16)=16/7#. Our perpendicular line is

#y=16/7x+b#. But this line passes through #(5,4)#. Then

#4=16/7·5+b#. Transposing terms we have #b=-52/7#

Finally, perpendicular line equation is #y=16/7x-52/7#

Mar 13, 2018

Answer:

#y=16/7x-52/7#

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=-7/16x" is in this form"#

#"with "m=-7/16#

#"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/(-7/16)=16/7#

#rArry=16/7x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(5,4)" into the partial equation"#

#4=80/7+brArrb=28/7-80/7=-52/7#

#rArry=16/7x-52/7larrcolor(red)"perpendicular equation"#