Question 279605
third equation is x + 6y >= -9


subtract x from both sides of this equation to get:


6y >= -x - 9


divide both sides of this equation by 6 to get:


y = (-1/6)x - (9/6)


graph the equation of y = -(1/6)x - (9/6)


the shaded area will be everything above or equal to that line.


any value of y above or on that line will be valid.


the graph will look like this:


{{{graph(600,600,-10,10,-10,10,-(1/6)*x - (9/6))}}}


your slope should have been -(1/6), and not -(9/6).


you solve your fourth equation in a similar manner.


your fourth equation is 3x-2y >= -7.


subtract 3x from both sides of this equation to get:


-2y >= -3x - 7


multiply both sides of this equation by (-1) to get:


2y <= 3x + 7


note that multiplying both sides of an inequality reverses the inequality.


if 5 > 3, then -5 < -3 for example.


your equation is now:


2y <= 3x + 7


divide both sides of this equation by 2 to get:


y <= (3/2)*x + (7/2)


graph the equation of y = (3/2)*x + (7/2)


your shaded area will be everything below or on that line.


any value of y below or on that line will be valid.


a graph of that equation looks like this:


{{{ graph(600,600,-10,10,-10,10,(3/2)*x + (7/2))}}}