How do you write an equation of a line passing through (1, 5), perpendicular to #y + 4x = 7#?

1 Answer
Mar 13, 2018

Answer:

#y=1/4x+19/4#

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"#

#"Rearrange "y+4x=7" into this form"#

#"subtract 4x from both sides"#

#ycancel(+4x)cancel(-4x)=-4x+7#

#rArry=-4x+7larrcolor(blue)"in slope-intercept form"#

#"with slope m "=-4#

#"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/(-4)=1/4#

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

#"To find b substitute "(1,5)" into the partial equation"#

#5=1/4+brArrb=20/4-1/4=19/4#

#rArry=1/4x+19/4larrcolor(red)"equation of perpendicular"#