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