# Math Help - write an equation

1. ## write an equation

Write an equation of the following line:

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

Thanks

2. Originally Posted by ecdino2
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: $x - 2y + 3 = 0 \implies y = \frac{1}{2}x + \frac{3}{2}$

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

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

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

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

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

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

3. Hello
I'have another solution :