Find the equation of a line that goes through the point (2,-3) and is perpendicular to the line y= -2/5x+6

Find the negative reciprocal of the given line's slope in order to determine what the slope of the line will be.

-2/5 -> -5/2 -> 5/2

Your line now looks like this: y = 5/2x + b

Now, substitute the given point into the y and x variables and solve for b.

   y = 5/2x + b
  -3 = 5/2(2) + b
  -3 = 5 + b
  -8 = b

You are now done. The line is y = 5/2x - 8.

To get a perpendicular line to y=-2/5x+6 all you need to do is get the negative reciprocal of the slope then use (2,-3) and point slope formula to get your new equation.

y=-2/5x+6 

m=-2/5   so new equation slope is m=5/2

y−b=m(x−a)   or y-y1=m(x-x1)

point is (2,-3)

plug and chug

y-(-3)=5/2(x-2)
y=5/2x-8