Question 521342
Given
Point (x, y)=(3,-6) 
Line: 4x+9y=7
Rearrange the equation according to equation of standard form 
4x+9y=7
9y=-4x+7
9y/9=(-4x+7)/9
y=(-4/9)x+7/9
Compare above equation with the equation of line slope-intercept form
y=mx+b

m=-4/9  and b=7/9
Slope of the given line m =-4/9 and y-intercept = b =7/9

Since required line is perpendicular, the multiplication of the slopes of both lines result in (-1), therefore the slope of the required line will be (9/4)
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Now we have a point (3,-6) and slope (9/4) of the required line we can easily find the required line put these values in the equation of slope-intercept form to find the y-intercept of the required line
y=mx+b
-6=(9/4)(3)+b
-6=27/4+b
-6-27/4=b
-24-27/4=b
-51/4=b
b=-51/4

y-intercept of the required line =b=-51/4
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Put the values of ‘m’ and ‘b’ in equation of the line slope-intercept form
y=mx+b
y=(9/4)x-51/4
Above equation is the required equation of the line
Red Line = y =(-4/9)x+7/9
Green Line = y =(9/4)x-51/4 

{{{ graph( 500, 500, -15, 15, -15, 15, y=-4x/9+7/9,y=9x/4-51/4) }}}