What is the equation of the line perpendicular to #y=-15/4x # that passes through # (-1,7) #?

1 Answer
May 9, 2018

Answer:

#y=4/15x+109/15#

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 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#

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

#"to find b substitute "(-1,7)" into the partial equation"#

#7=-4/15+brArrb=105/15+4/15=109/15#

#rArry=4/15x+109/15larrcolor(red)"perpendicular equation"#