Question

Which shows the graph of a solution set of y>-1/2x–3

Answer 1

`y > -(1)/(2)x-3\\\\y=-(1)/(2)x-3\\\\for\ x=0\to y=-(1)/(2)\cdot0-3=3\to(0; -3)\\\\for\ x=-6\to y=-(1)/(2)\cdot(-6)-3=3-3=0\to(-6;\ 0)`

Answer 2

Explanation:

We have been given an inequality
`y>-(1)/(2)x-3`. We are asked to find the graph of our given inequality.

We can see that our given inequality has a greater than (>) sign, so the boundary line of our given inequality would be dotted line.

So boundary line for our given inequality would be:
`y=-(1)/(2)x-3`.

Since slope of boundary line is negative, so boundary line would be a decreasing line.

Now, we will check point (0,0) in our given inequality to find the shaded region.

`0>-(1)/(2)(0)-3`

`0>0-3`

`0>-3`

Since point (0,0) satisfies our inequality, so solution for our given inequality will include point (0,0) that is origin.

Please find the attachment for graph of solution of our given inequality.