How do you write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2, 6)?

1 Answer
Mar 7, 2018

Answer:

#y=1/4x+11/2#

Explanation:

#"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#

#"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=-4x" is in this form"#

#"with slope "m=-4#

#rArrm_(color(red)"perpendicular")=-1/(-4)=1/4#

#rArry=1/4x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(2,6)" into the partial equation"#

#6=1/2+brArrb=12/2-1/2=11/2#

#rArry=1/4x+11/2larrcolor(red)"in slope-intercept form"#