Question

Which of the following is the correct solution to the linear inequality y > 1/3x - 2? What does the inequality look like graphically?

a) y > 1/3x - 2; Shaded area above the line
b) y < 1/3x - 2; Shaded area below the line
c) y ≥ 1/3x - 2; Shaded area above and on the line
d) y ≤ 1/3x - 2; Shaded area below and on the line

Answer 1

The correct solution is option a), where y is greater than 1/3x - 2 and graphically represented by the shaded area above the dashed line of the equation y = 1/3x - 2.

Step-by-step explanation:

The solution to the linear inequality y > 1/3x - 2 is represented by the area above the line of the equation y = 1/3x - 2 in a graph. When graphed, this inequality will show a line with a positive slope that crosses the y-axis at -2 (as indicated by the y-intercept in the equation). Since the inequality is 'greater than' (>) and not 'greater than or equal to' (≥), the line itself is not included in the solution set, which means the line is drawn with a dashed line. Therefore, the correct answer is option a), which indicates that the shaded area on the graph should be above the line.