Answer:
5x +3y = -40
Explanation:
You want an equation for the line through P(-8, 0) perpendicular to 3x -5y = 6.
Perpendicular line
The line perpendicular to ax +by = c can be written as ...
-bx +ay = c'
where c' is chosen so that the given point satisfies the equation.
For a=3, b=-5, this is ...
5x +3y = c'
For (x, y) = (-8, 0), the constant is ...
5(-8) +3(0) = c' = -40
The equation of the perpendicular line is 5x +3y = -40.
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Additional comment
The perpendicular line can be either of ...
-bx +ay = c'
bx -ay = c'
As a rule, we like the leading coefficient to be positive, so we choose the form of the equation to make that true. If 'a' and 'b' have a common factor, it usually works well to divide both coefficients by that factor, so they end up mutually prime.
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