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.