Given that, two lines having the same y-intercept are perpendicular. And the given equation is,
[tex]y=-\frac{4}{5}x+6[/tex]Here, slope is -4/5, and y intercept is 6.
The slope of the perpendicular line is the negative reciprocal.
Therefore the equation for the perpendicular line is,
[tex]y=\frac{5}{4}x+6[/tex]