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

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