How do you write an equation in slope intercept form perpendicular to y=1/2x-4, contains (4,1)?

2 Answers
Mar 19, 2017

Answer:

#y=-2x+9#

Explanation:

An equation in the form #y=color(green)mx+color(blue)b# is in slope intercept form with a slope of #color(green)m#

Therefore #y=color(green)(1/2)x-4# has a slope of #color(green)(1/2)#

If a line has a slope of #color(green)m# then any line perpendicular to it has a slope of #color(magenta)(-1/m)#

Therefore any line perpendicular to #y=color(green)(1/2)x-4#
must have a slope of #color(magenta)(-2)#
and a slope-intercept form of #y=(color(magenta)(-2))x+color(blue)b# for some constant #color(blue)b#

If #(color(red)x,color(orange)y)=(color(red)4,color(orange)1)# is to be a point on the required perpendicular line then
#color(white)("XXX")color(orange)1=(color(magenta)(-2)) * color(red)4 +color(blue)b#

#color(white)("XXX")rarr color(blue)b=9#

and the equation of the required perpendicular line is
#color(white)("XXX")y=color(magenta)(-2)x+color(blue)9#

Mar 19, 2017

Answer:

#y=-2x+9#

Explanation:

#y=1/2x-4" is in "color(blue)"slope-intercept form"#

#"That is " y=color(red)(m)xcolor(blue)(+b) " where " color(red)(m)# represents the slope and #color(blue)(+b)# the y-intercept.

#rArr" slope "=m=1/2#

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

#rArrm_("perpendicular")=-1/(1/2)=-2#

The equation can be written partially as #y=-2x+b#

To calculate b substitute (4 ,1) into the partial equation.

#rArr(-2xx4)+b=1#

#rArrb=1+8=9#

#rArry=-2x+9larrcolor(red)" in slope-intercept form"#