# What is the equation of the line perpendicular to #y=-5/9x # that passes through # (-7,3) #?

##### 1 Answer

Jan 16, 2016

5y - 9x + 48 = 0

#### Explanation:

One of the forms of the equation of a straight line is y = mx + c where m represents the gradient and c , the y-intercept.

the line

# y = -5/9 x# is in this form with c = 0 and m =

#-5/9 # When 2 lines are perpendicular then the product of their gradients :

# m_1m_2 = - 1 # The gradient of the perpendicular line is :

# -5/9 xx m_2 = - 1 #

#rArr m_2 =- 1/(-5/9) = 9/5 # equation : y - b = m(x - a ) , m =

#9/5 , (a , b ) = ( - 7 , 3 )#

#rArr y - 3 = 9/5 (x - 7 ) # multiply both sides by 5 to eliminate fraction :

#5y - 15 = 9x - 63 # equation of perpendicular line is 5y - 9x + 48 = 0