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what is an equation of the line that passes through the point (-4, -6) and is perpendicular to the line 4x+5y=25 ?

Sagot :

sqdancefan

Answer:

  5x -4y = 4

Step-by-step explanation:

An equation for the perpendicular line can be found by swapping the x- and y-coefficients, and negating one of them. The constant changes to a value so that the equation is satisfied at the given point.

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new line

Swapping the coefficients gives us ...

  5x +4y = c . . . . . for some constant c

Negating the y-coefficient (so the x-coefficient remains positive) gives ...

  5x -4y = c

constant

Putting (x, y) = (-4, -6) into the equation gives us the value of c:

  5(-4) -4(-6) = c

  -20 +24 = c = 4

equation

The line perpendicular to the given line and through the point (-4, -6) will have equation ...

  5x -4y = 4

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