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

1 Answer
Apr 21, 2017

Answer:

#y=-4x-24#

Explanation:

#y=1/4x" is in "color(blue)"slope-intercept form"# that is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#
where m represents the slope and b, the y-intercept.

#rArry=1/4x" has slope " =m=1/4#

The slope of a line perpendicular to this is #color(blue)"the negative reciprocal"# of m

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

The equation of a line in #color(blue)"point-slope form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#
where # (x_1,y_1)" is a point on the line"#

#"using " m=-4" and " (x_1,y_1)=(-7,4)#

#y-4=-4(x-(-7))#

#rArry-4=-4(x+7)larrcolor(red)" in point-slope form"#

#"distributing and simplifying gives"#

#y-4=-4x-28#

#rArry=-4x-24larrcolor(red)" in slope-intercept form"#