Question

which is the graph of the linear equation 2x - 3y < 12?​

Answer 1

It is the third choice.
Dotted line because there’s no equal sign.
Plug in (0,0) to check a point...2(0)-3(0)=0 which is less than 12 and is shaded.

Answer 2

For this case, we must indicate the shaded region that represents the following inequality:

$2x-3y <12$

First we must observe that the inequality is open, that is, it does not include the "=", therefore we discard the first and fourth option, where the line is not dotted at the border of the region.

Now, we substitute the point $(x, y) = (0,0)$ to know if the inequality is met:

$2 (0) -3 (0) <12\\0-0 <12\\0 <12$

The inequality is met, then the point (0,0) belongs to the shaded region, so the correct option is region 3.

Answer:

Option C