How do you write an equation in slope intercept form perpendicular to y=1/2x-4, contains (4,1)?
2 Answers
Explanation:
An equation in the form
Therefore
If a line has a slope of
Therefore any line perpendicular to
must have a slope of
and a slope-intercept form of
If
and the equation of the required perpendicular line is
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"#