What is the equation of the line that passes through #(-1,4)# and is perpendicular to the line that passes through the following points: #(-2,2),(5,-6) #?

1 Answer
Mar 11, 2016

Answer:

#8y = 7 x + 39#

Explanation:

The slope m, of the line passing through #(x1,y1) & (x2,y2)# is

#m = (y2 - y1) / (x2 - x1)#
Thus the slope of the line passing through #(-2,2) & (5, -6)# is
#m = (-6 - 2) / ((5 - (-2))# = #-8 / 7#
Now if the slope of two lines which are perpendicular to each other are m and m', we have the relationship
#m * m' = -1#
So, in our problem, the slope, m2, of the first line = #-1 / (-8 / 7)#
= #7 / 8#
Let the equation of the line be #y = m2x + c#
Here, #m2 = 7 / 8#
So the equation is #y = 7 / 8 x + c#
It passes through the points, #(-1,4)#
Substituting the x and y values,
#4 = 7 / 8 * (-1) + c#
or #c = 4 + 7 / 8 = 39 / 8#
So the equation is
#y = 7 / 8 x + 39 / 8#
or #8 y = 7 x + 39#