Find the equation of the line described below?

The slopes of perpendicular lines are negative inverses
the constant depends on which point the line goes through.

Therefor swap the coefficients, change one of the signs, and leave the constant for the next step
5x + 3y = c

To find the constant, "c", plug in the given point (-5, -8)
5(-5) + 3(-8) = c
-25 + (-24) = c
c = -49

This yields the equation as
5x + 3y = -49
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Slope intercept form is
y = mx + b

5x + 3y = -49

Subtract 5x from both sides
3y = -5x - 49

Divide both sides by 3
y = -(5/3)x - 49/3 <–––––– slope intercept equation of perpendicular line through (-5, -8)





 

m_perpindicular = -1 / m_parallel
a parallel line has the same slope
3x -5y =11
-5y = -3x + 11
y = (-3/-5)x - 11/5
y = (3/5)x- (11/5)
parallel slope = (3/5)
m_perpindicular = -1 / m_parallel = -1/ (3/5) = -5/3
point(-5,-8)
y= mx +b
b = y- mx
m = -5/3
b =y - (-5/3)x
b = y + (5/3)x
b = -8 + (5/3)(-5) = -8 + -25/3 = -49/3 = -16 1/3
y = (-5/3)x -16 1/3
or
y = (-5/3)x - 49/3

The perpendicular equation is: y = (-5/3)x - 49/3