what is the equation of the line perpendicular to 2x-5y+4=0, with the same x-intercept as 2x+y-10=0

Answer 1

The perpendicular line would have a slope equal to the inverse of the original line, so

2x-5y+4=0 -> 2x+4=5y -> (2/5)x+4/5=y gives a slope of 2/5 so the other line has a slope of -2/5.

By the 2nd part, it would pass thru (5,0). From there, you can directly write the equation in point-slope form.