Question

What is the equation of the line that is perpendicular to y=1/2+3 and passes through the point (10,-5)

Answer 1

$k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\Rightarrow m_2=-\dfrac{1}{m_1}$

We have:
$k:y=\dfrac{1}{2}x+3;\ l:y=mx+b\\\\k\ \perp\ l\iff m=-\dfrac{1}{\frac{1}{2}}=-2\\\\therefore\ l:y=-2x+b.$

The line l passes throught the point (10;-5). Subtitute the value of coordinates to the equation:

$-5=-2\cdot10+b\\\\-20+b=-5\ \ \ \ |add\ 20\ to\ both\ sides\\\\b=15$

Answer: y = -2x + 15.