Answer:
The perpendicular line passing through the point (7,10) is
2 x+y-24=0
Step-by-step explanation:
Step :1
perpendicular condition :-
The condition of perpendicular lines are [tex]m_{1} m_{2} = -1[/tex]
The given line is [tex]y= \frac{1}{2}x-9[/tex]and given point is (7,10)
the standard form of straight line is y=m x+c
The given line is y= \frac{1}{2}x-9
here m = \frac{1}{2}
now by using perpendicular condition solving the slope of perpendicular line is [tex]m_{1} m_{2} =-1[/tex]
[tex]m_{2} = - \frac{1}{m_{1} }[/tex]
[tex]m_{2} = \frac{-1}{\frac{1}{2} }[/tex]
[tex]m_{2} = -2[/tex]
straight line equation
Step 2 :-
The equation of the straight line having slope m=-2 and passing through the point (7,10) is
[tex]y-y_{1} = m (x-x_{1}[/tex])
There fore the equation of perpendicular straight line is
y-10 = -2 (x-7)
[tex]y-10 = -2 x+14[/tex]
Final answer
The equation of perpendicular straight line is
2 x+y-24=0
