Step-by-step explanation:
A line perpendicular to another has slope
[tex]m2 = - \frac{1}{m1} [/tex]
Where , m1 is the slope of the given line
and m2 is the slope of the line perpendicular to the given line !!
Given equation of line :- y = (5/4)x + 2
comparing it with equation of straight line
i.e, y = mx + c
Where m is slope of the line and c is y intercept !!
So, comparing we get m1 = 5/4
and c = 2
[tex]then \\ \: m2 = \frac{1 - }{( \frac{5}{4} ) } \\ m2 = \frac{ - 4}{5} [/tex]
Also, the perpendicular line passes through the point ( 10 , - 5 )
x1 = 10
y1 = -5
Equating of the line :-
( y - y1 ) = m ( x - x1 )
So,
( y - ( -5) ) = ( -4/5) ( x - 10 )
( y + 5 ) = (-4/5) ( x - 10 )
5y + 25 = -4x + 40
4x + 5y - 15 = 0
Is ,the required equation !!
