To find the slope of the line perpendicular to 5x-2y=-18. I would suggest changing the equation to point slope form or y=(5x/2)+9. The slope of the line perpendicular is the negative reciprocal. To find the reciprocal flip the slope of 5/2 to 2/5 and add a negative sign to -2/5. Now to find the constant of the equation solve the point slope form of y-4=-2/5(x-10) this simlifies to y=-2/5x+8. Your answer is the y=-2/5x+8.