Hi Alex
Is there a point that your perpendicular passes through? If not you can get started with the information below.
The line perpendicular to
y-4=-2/3(x-6)
In slope intercept will have a slope, m the is the negative inverse (-2/3) but first we should put
y-4=-2/3(x-6)
Into Slope intercept form
y = (-2/3)x + 4 + 4
y= (-2/3)x + 8
The slope m above is -2/3
The slope, m, for the perpendicular line is 3/2
y = (3/2)x + b
We need a point that this perpendicular passes through in order to solve for b
If b = 0, then
y = (3/2)x is perpendicular to y= (-2/3)x + 8
You can check this by graphing both at Desmos.com
I hope this help you on your way to define the complete line including the y intercept, b.
