Final answer:
To graph the inequality y > x - 1, graph the boundary line y = x - 1 with a slope of 1 and a y-intercept of (0, -1) using a dashed line. Then, pick a test point to determine which side of the line to shade; shade above the line for the area where the inequality is true.
Step-by-step explanation:
To graph the inequality y > x - 1, we start by graphing the boundary line, which would be y = x - 1. This line has a slope of 1 and a y-intercept of (0, -1).
First, plot the y-intercept at (0, -1) on the graph. Then, use the slope to find another point. Since the slope is 1, it means for every one unit you move to the right along the x-axis, move one unit up along the y-axis. So, from (0, -1), moving right 1 unit and up 1 unit will land us at (1, 0). Plot this point as well.
Draw a dashed line to connect these points since the inequality is strict (y > x - 1), not including the line itself. If it were 'greater than or equal to', we'd draw a solid line instead.
To determine which side of the line is the solution to the inequality, you can pick a test point not on the line (e.g., (0,0)) and plug it into the inequality. Since 0 is not greater than 0 - 1, the test point doesn't satisfy the inequality, meaning the solution is on the other side of the line. Shade the area above the line to indicate all points where y is greater than x - 1.