Question

Which is the graph of the linear equation 1/2x-2y>-6

Answer 1

$\dfrac{1}{2}x-2y > -6\ \ \ \ |-\dfrac{1}{2}x\\\\-2y > -\dfrac{1}{2}x-6\ \ \ |change\ signs\\\\2y > \dfrac{1}{2}x+6\ \ \ \ |:2\\\\y > \dfrac{1}{4}x + 3$
$y=\dfrac{1}{4}x+3\\\\for\ x=0\to y=\dfrac{1}{4}\cdot0+3=3\to(0;\ 3)\\\\for\ x=-4\to y=\dfrac{1}{4}\cdot(-4)+3=-1+3=2\to(-4;\ 2)$