Question

consider the line 8x-5y=-4
find the equation of the line that is perpendicular to this line and passes through the point (-4,-4)

find the equation of the line that is parallel to this line and passes through the point (-4, -4)

i keep getting different answers on the perpendicular and parallel equations can anybody help?

Answer 1

5 y = 8 x + 4
y = (8/5) x + 4/5
so slope is 8/5
so slope of perpendicular is -5/8
form is
y = - 5x/8 + b
goes through (-4,-4)
-4 = -5 (-4)/8 + b
b = -4 - 20/8
b = -4 - 5/2
b = -8/2-5/2 = -13/2
so
y = - 5 x/8 -13/2
or
8y = -5 x - 52

Now parallel line
slope = 8/5
y = 8 x/5 + b
-4 = -32 /5 + b
-20/5 = -32 /5 + b
b = 12 /5
so
y = 8 x/5 + 12/5
or
5 y = 8 x + 12