Question

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

Answer 1

The graph of the linear inequality 2x-3y < 12 is a shaded region below the line 2x - 3y = 12. To graph this inequality, plot the line and choose a test point to determine which side of the line is shaded.

Step-by-step explanation:

The graph of the linear inequality 2x – 3y < 12 is a shaded region below the line 2x - 3y = 12. To graph this inequality, we can start by graphing the line 2x - 3y = 12. This line has a slope of 2/3 and a y-intercept of -4, so we can plot those points and connect them to create the line. Next, we can choose a test point that is not on the line, such as (0,0), and substitute its x and y values into the inequality. If the inequality is true, then the shaded region is below the line. If the inequality is false, then the shaded region is above the line. In this case, when we substitute (0,0) into the inequality, we get 0 < 12, which is true. Therefore, the shaded region is below the line.

Answer 2

2x-3y<12 subtract 2x from both sides

-3y<-2x+12 divide both sides by -3 (and reverse inequality sign because of division/multiplication by a negative value)

y>(2x-12)/3

So the graph is the third choice, the one with the shaded area above the line y=(2x-12)/3 with the line dashed. The dashed line indicates that the line itself in not in the solution set.