# How do you find the slope of a line perpendicular to V(3, 2), W(8, 5)?

##### 2 Answers

See a solution process below:

#### Explanation:

First, find the slope of the line V-W. The slope can be found by using the formula:

Where

Substituting the values from the points in the problem gives:

Now, let's call the slope of the perpendicular line

The slope of a perpendicular line is the negative inverse of the slope of the line it is perpendicular to, or:

Substituting for

The slope of the line perpendicular to V-W is

#### Explanation:

#"to calculate the slope of the line VW use the "color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#

where m represents the slope and# (x_1,y_1),(x_2,y_2)" are 2 coordinate points"#

#"the points are " (x_1,y_1)=(3,2),(x_2,y_2)=(8,5)#

#rArrm_(color(red)(VW))=(5-2)/(8-3)=3/5#

#" the slope of a line perpendicular to VW is"#

#m_(color(red)"perpendicular")=-1/m_(color(red)(VW))#

#rArrm_(color(red)"perpendicular")=-1/(3/5)=-5/3#