Which is the graph of the linear inequality 2x – 3y < 12?

Question: Which is the graph of the linear inequality 2x – 3y < 12?

Answer:

The solution of the given linear inequality, 2x – 3y < 12 would be in the form of a line with a region being hatched at the lower side of the line.

To draw the linear inequation 2x – 3y < 12 on the graph, the boundary line 2x – 3y = 12 needs to be graphed first. The line drawn can be put to the form of y = (2/3)x – 4. The line is 2/3 slope and has a y-intercept of -4. We can plot this line by using two points: Its two vertices are at the coordinates: < (0, -4), (3, -2)> After setting out the boundary line, we are required to identify which side of the line is signifying the solution set. Therefore, it is evident that (0, 0) is in the region we are exploring hence 0 < 12 is true meaning that the region including the origin is the answer to the inequality statement in question below the line hence shading is systematic there. The line of the equation 2x – 3y = 12 is drawn as a strict line if the inequality is less than (<) or as a dashed if it’s less than or the shaded area below the broken line is the set of all points (x, y) that make the inequality 2x – 3y < 12 true.