<PRE><B>Question 654493</B>
Find the value of k so that the line containing the points (-4,k) and (8,-4)
 is perpendicular to the line y=2/5x+4.
:
The slope of the given equation: m1 = {{{2/5}}}
Find the slope (m2) of the given coordinates
The slope formula m = {{{(y2-y1)/(x2-x1)}}}
Assign the values as follows
x1=-4, y1=k
x2=8, y2=-4
m2 = {{{(-4-k)/(8-(-4))}}} = {{{((-4-k))/12}}}
:
We know the slope relationship between perpendicular lines is m1*m2 = -1
{{{2/5}}}*{{{((-4-k))/12}}} = -1
cancel 2 into 12
{{{1/5}}}*{{{((-4-k))/6}}} = -1
{{{((-4-k))/30}}} = -1
multiply both sides by -30, also gets rid of all those negatives
4 + k = 30
k = 30 - 4
k = 26
:
Use this value for y1, find the slope (m2) of the new equation,
Find the equation using the point/slope formula, y-y1 = m(x-x1)
See that it is perpendicular to y = {{{2/5}}}x + 4</PRE>