Final answer:
To identify the linear inequality from a graph, analyze the line's slope, y-intercept, and the region's shading. Without the graph, we can't make a definitive match to the given options.
Step-by-step explanation:
To determine which linear inequality is represented by the graph, we need to consider the characteristics of each given inequality and how they would translate graphically. A linear inequality resembles the equation of a line, y = a + bx, except inequality symbols are used instead of an equal sign. The graph of a linear inequality also includes a shaded region representing all the (x,y) coordinates that satisfy the inequality.
For option (a), y > x - 2, this would correspond to a line with a slope (b) of 1 and a y-intercept (a) of -2. The inequality '>' indicates that the area above the line is shaded. As for option (b), 10y ≤ 2x + 2, after dividing by 10 to solve for y, we'd get a positive slope of 1/5 and a y-intercept of 0.2, with the region below the line shaded due to the '≤' symbol. Option (c) is incomplete and thus cannot represent a linear inequality. Lastly, option (d), y < x - 1, would have a positive slope of 1, a y-intercept of -1, and the region below the line shaded because of the '<' symbol.
To match the inequality with a given graph, you'd look for these characteristics: the slope direction (upward for positive, horizontal for no slope, downward for negative), the position of the y-intercept, and the shading direction (above or below the line). Without the graph, we cannot definitively determine which of these inequalities it represents.