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.