Question 139826
A line passing through (-4,4) and (x,-8) is perpendicular to a line with slope 5/12. Find the value of x.
:
m1 = slope of the given coordinates
m2 = 5/12
;
We know that the relationship of the slopes of perpendicular lines is:
m1 * m2 = -1
m1 *{{{5/12}}} = -1
Multiply equation by 12:
m1 * 5 = -12
m1 = {{{-12/5}}}
:
Using the slope formula;  (y2-y1)/(x2-x1) = m:
{{{(-8 - 4)/(x -(-4))}}} = {{{-12/5}}}
:
You can see that x has to = 1, but here is the algebra to solve it:
{{{(-12)/((x+4))}}} = {{{-12/5}}}
neg on both sides:
{{{12/((x+4))}}} = {{{12/5}}}
cross multiply, solve for x:
12(x+4) = 12 * 5
12x + 48 = 60
12x = 60 - 48
12x = 12
x = 1