What is the equation of the line perpendicular to #y=15/4x # that passes through # (-2,7) #?

1 Answer
May 23, 2018

Answer:

#y=-4/15x+97/15#

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=15/4x" is in this form"#

#"with "m=15/4" and "b=0#

#"given the equation of 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/(15/4)=-4/15#

#y=-4/15x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(-2,7)" into the partial equation"#

#7=8/15+brArrb=105/15-8/15=97/15#

#y=-4/15x+97/15larrcolor(red)"equation of perpendicular line"#