Final answer:
To identify the linear inequality corresponding to the graph, examine the line's slope and y-intercept. The graph's representation of the inequality (solid or dashed line) and shading on one side will indicate the correct inequality option. Without seeing the graph, a definitive answer cannot be given.
Step-by-step explanation:
To determine which linear inequality is represented by the graph, we need to examine the slope (rise over run) and the y-intercept of the graph. The y-intercept is the value of y where the line crosses the y-axis and the slope of the line indicates how steep the line is and whether it goes up or down as we move from left to right.
A positive slope means the line slopes upward, a slope of zero indicates a horizontal line, and a negative slope means the line slopes downward. Options (a) y ≤ 3/2x + 3 and (c) y < 3/2x + 3 both have a positive slope of 3/2, while options (b) y > 2/3x + 3 and (d) y ≥ 2/3x + 3 have a positive slope of 2/3.
The inequality also involves the type of line on the graph. If the line is solid, then the inequality is either ≤ or ≥; if the line is dashed, then the inequality is < or >.
Without viewing the graph, we cannot definitively determine which inequality it represents. However, by comparing the slopes and y-intercepts provided in the options, it's possible to narrow down the choice if we know the characteristics of the graph. Additionally, if the graph has shading, it could indicate which side of the line the inequality represents (above or below).