Write an equation in slope-intercept form for the line that passes through (-1, 4) and is perpendicular to the graph of the equation: y=3x+5 ?

1 Answer
Mar 24, 2018

#y=(-1/3)x-(1/3)+4#

Explanation:

Provided that the line passes through #(-1,4)# and is perpendicular to line #y=3x+5#
We know
The product of gradients of two mutually perpendicular lines is #-1#
So
Let #m_1 = 3#
We have to find #m_2#
So #m_1 ×m_2 =-1#
# or, 3×m_2 =-1#
Hence #m_2 = -1/3#
Choose #m=-1/3#
By point slope forme
#(y-y_1)=m (x-x_1)#
# or, (y-4)=(-1/3)(x-(-1)#
# or, (y-4)=(-1/3)x-(1/3)#
# or, y=(-1/3)x-(1/3)+4# is the required equation.