What is the equation of the line perpendicular to #y=-7/16x # that passes through # (5,4) #?
2 Answers
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Explanation:
If a line has the equation
In our case
Finally, perpendicular line equation is
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"#