Sketch the graph of the linear inequality $3x-2y\le -6$ .

A)
B)
C)
D)
E)

To graph the linear inequality $3x-2y\le -6$ , we first need to graph the line $3x-2y=-6$ . We do this by finding the $x$ and $y$ intercepts.

Setting $x=0$ , we get $0-2y=-6$ , so $y=3$ . Therefore, the $y$ -intercept is $(0,3)$ .

Setting $y=0$ , we get $3x-0=-6$ , so $x=-2$ . Therefore, the $x$ -intercept is $(-2,0)$ .

Plotting these two points and drawing a straight line through them, we get:

Graph:

Now, we need to shade the region below this line to represent the inequality $3x-2y\le -6$ . We can test a point inside this region - for example, $(0,0)$ - to see if it satisfies the inequality.

$3(0)-2(0)\le -6$

$0\le -6$ , which is false.

Since $(0,0)$ does not satisfy the inequality, we need to shade the region on the other side of the line. This is the region below the line.

Therefore, the correct graph is:

Graph: 11ed7ae8_3727_cdcc_88db_070308ddb142_TBX8968_11

So, the answer is C.