# What is the slope of any line perpendicular to the line passing through #(15,-22)# and #(12,-15)#?

##### 1 Answer

Oct 2, 2016

#### Explanation:

Given 2 perpendicular lines with slopes

#m_1" and " m_2# then

#color(red)(bar(ul(|color(white)(a/a)color(black)(m_1xxm_2=-1)color(white)(a/a)|)))# We require to calculate

#m_1# using the#color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))#

where# (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"# The 2 points here are (15 ,-22) and (12 ,-15)

#rArrm_1=(-15-(-22))/(12-15)=7/(-3)=-7/3# Thus

#-7/3xxm_2=-1#

#rArrm_2=(-1)/(-7/3)=3/7# Hence the slope of any line perpendicular to the line passing through the 2 given points is

#m=3/7#