How do i find the equation of a perpendicular line segment with 2 endpoints given to be that also share the same x-intercept

Question

"Determine the equation of a line perpendicular to the line segment with endpoints (-1, 6) and (5, -3) and sharing the same x-intercept as 2x-5y=0."

Answer 1

x interept of 2x-5y= 0 is the x value when y=0, x=0 also, x intercept is the origin

the line through the two points has slope = 9/-6 =-3/2

the perpendicular line has a negative inverse slope = 2/3

the perpendicular line with x interept = origin is

y = (2/3)x in slope intercept form, with y intercept =0

or

3y = 2x

or

2x-3y = 0 in standard form