Question 975860
The first line is y=(4/5)x -(23/5)
The second line MUST have a slope of (-5/4)
point slope formula
y-7=(-5/4)(x+3)
y=(-5x/4)+3

graph below shows these two plus yours (in blue); green is the perpendicular line to the original.

{{{graph(300,300,-10,10,-10,10,(4/5)x -(23/5),(-5x/4)+3,(5x/4)-(13/4))}}}