Question 79984
A line passing through (5,-8) and (9,y) is perpendicular to a line with slope -4/9. Find the value of y.
:
Let m1 = (-4/9)
:
Find the slope m2 from the given coordinates; x1=5, y1=-8; x2=9; y2=y:
m2 = {{{((y - (-8)))/((9 - 5))}}} = {{{((y+8))/4}}}
:
We know the slope relationship of perpendicular lines is: m1 * m2 = -1
Substitute for m1 and m2:
:
{{{(-4/9)*((y+8)/4)}}} = -1
:
Conveniently, the 4's cancel so we have:
{{{-((y+8)/9)}}} = -1
: 
{{{((y+8)/9)}}} = +1; multiplied by -1
:
y + 8 = 9; multiplied equation by 9
:
y = 9 -8
:
y = 1
:
Therefore m2 = {{{((y+8))/4}}} = {{{((1+8))/4}}} = {{{9/4}}}