# 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"#