Answer:
y-7=-(4/3)(x-5) (point slope form)
y=-(4/3)x+(41/3) (slope intercept form)
4x+3y-41=0 (general form)
Step-by-step explanation:
step 1
Find the slope of the perpendicular line to 4y-3x+9=0
If two lines are perpendicular, then the product of their slopes is equal to -1
4y-3x+9=0
4y=3x-9
y=(3/4)x-9/4 -----> the slope is m=3/4
The perpendicular slope is
m*(3/4)=-1
m=-4/3
step 2
Find the equation of the line into slope point form
y-y1=m(x-x1)
we have
(x1,y1)=(5,7)
m=-4/3
substitute
y-7=-(4/3)(x-5) ----> equation of the line into point slope form
Convert to slope intercept form ----> y=mx+b
y-7=-(4/3)(x-5)
y-7=-(4/3)x+(20/3)
y=-(4/3)x+(20/3)+7
y=-(4/3)x+(41/3) -----> equation of the line into slope intercept form
Convert to general form ----> Ax+By+C=0
y=-(4/3)x+(41/3)
Multiply by 3 both sides
3y=-4x+41
4x+3y-41=0 -----> equation of the line in general form
