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

##### 1 Answer

May 2, 2018

#### 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=5/16x" is in this form"#

#"with slope "=5/16" and y-intercept "=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/(5/16)=-16/5#

#rArry=-16/5x+blarrcolor(blue)"is the partial equation"#

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

#4=16+brArrb=4-16=-12#

#rArry=-16/5x-12larrcolor(red)"equation of perpendicular"#