Write the equation of the line that is perpendicular to the line 8y−16=5x through the point (5,-5).

y = -(8/5)x + 3

Step-by-step explanation:

Step 1:  Rewrite the given equation into slope-intercept form by solving for y

8y−16=5x

   8y = 5x + 16

      y = (5/8)x + 2

Perpendicular lines have slopes that are opposite reciprocals of each other.  That means you take the slope, flip the fraction, and change the sign.

Here our given line is y = (5/8)x + 2 so the slope 5/8

The opposite reciprocal of 5/8 is -8/5

We set up the equation

y = -(8/5)x + b      

  we are given a point (x, y) of (5, -5), so plug that in and solve for b

-5 = -(8/5)(5) + b

    -5 = -8 + b

     3 = b  

So our equations is  y = -(8/5)x + 3

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step-by-step explanation: