Question

Write an equation of the line that passed through (7,10) and is perpendicular to the line y=1/2x-9

Answer 1

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 $m_{1} m_{2} = -1$

The given line is $y= \frac{1}{2}x-9$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 $m_{1} m_{2} =-1$

     $m_{2} = - \frac{1}{m_{1} }$

     $m_{2} = \frac{-1}{\frac{1}{2} }$

    $m_{2} = -2$

straight line equation

Step 2 :-

The equation of the straight line having slope m=-2 and passing through the point (7,10) is

$y-y_{1} = m (x-x_{1}$)

There fore the equation of perpendicular straight line is

y-10 = -2 (x-7)

$y-10 = -2 x+14$

Final answer

The equation of perpendicular straight line is

2 x+y-24=0