# write an equation

#### ecdino2

Write an equation of the following line:

a line perpendicular to x - 2y + 3 = 0 and passing through the point (4;-1)

Thanks

#### harish21

Write an equation of the following line:

a line perpendicular to x - 2y + 3 = 0 and passing through the point (4;-1)

Thanks
The equation of the line given is: $$\displaystyle x - 2y + 3 = 0 \implies y = \frac{1}{2}x + \frac{3}{2}$$

thse slope of this line is $$\displaystyle \frac{1}{2}$$

now the equation of the line passing through (4,-1) is:

$$\displaystyle y-(-1) = m (x-4)$$ ; where m is the slope.

these two lines are perpendicular if the product of their slopes is -1, that is,

$$\displaystyle \frac{1}{2} \times m = -1$$

find m and fit it in the second equation to find the equation of the line.

Last edited:
ecdino2

#### dhiab

Hello
I'have another solution :