# What is the equation of the line perpendicular to #y=-3/11x # that passes through # (8,7) #?

##### 1 Answer

Feb 1, 2016

3y - 11x +67 = 0

#### Explanation:

The equation of the line is of the form : y - b = m(x - a )

where m represents the gradient and (a,b) a point on the line.

Here (a , b) =(8 , 7) is given but require m.

When 2 lines are perpendicular to each other, the product of

their gradients is - 1 .

# m_1.m_2 = -1 # let

#m_1 = - 3/11 color(black)( " the gradient of given line ") # then

# m_2 color(black)(" is gradient of perpendicular line") # hence

# m_2 = -1/m_1 =( -1)/(-3/11) = 11/3# equation : y - 7

# = 11/3 ( x - 8 )# (multiply by 3 to eliminate fraction )

hence 3 y - 21 = 11x - 88

# rArr3 y - 11x + 67 = 0 #