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

Question

Quizplus · Accepted Answer

To graph the linear inequality $3 x - 2 y \leq - 6$, we first need to graph the line $3 x - 2 y = -6$. 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: 11ed7ae8_3727_cdcc_88db_070308ddb142_TBX8968_11

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

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

$0 \leq - 6$, 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.

Sketch the Graph of the Linear Inequality 3x−2y≤−63 x - 2 y \leq - 63x−2y≤−6

Sketch the Graph of the Linear Inequality $3 x - 2 y \leq - 6$