Final answer:
The correct graph for the linear inequality 2x - 3y < 12 is B. y < 2/3x - 4, which has a negative slope and the area below the line is shaded.
Step-by-step explanation:
To determine which graph represents the linear inequality 2x - 3y < 12, let us first convert the inequality into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
- Start by moving the term with x to the other side of the inequality: -3y < -2x + 12.
- Then, to isolate y, divide both sides of the inequality by -3, remembering to reverse the inequality sign because we're dividing by a negative number. This gives us y > 2/3x - 4.
The correct answer is B. y < 2/3x - 4 because reversing the inequality after dividing by -3 changes the symbol from '>' to '<'. The graph of this inequality will be a line with a slope of 2/3 and a y-intercept of -4, and the region below this line will be shaded to represent all the points (x, y) that satisfy the inequality.