Final answer:
To graph the inequality y < 3x - 7, plot the boundary line with a slope of 3 and a y-intercept of -7, use a dashed line because points on the line are not included, and shade the area below the line as it represents the solution set.
Step-by-step explanation:
To graph the inequality y < 3x - 7, first graph the corresponding boundary line y = 3x - 7. This line has a slope of 3 and a y-intercept of -7. To find the slope and y-intercept, you can compare the equation to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. The slope of 3 means that for every 1 unit you move horizontally to the right on the x-axis, you move up 3 units on the y-axis.
Start by plotting the y-intercept (0,-7) on the graph. Then, use the slope to find another point on the line. For example, from the y-intercept, move 1 unit to the right (positive direction on the x-axis) and 3 units up (positive direction on the y-axis) to reach the point (1,-4). Plot this point and draw a straight line through the two points.
Since the inequality is y < 3x - 7 and not y ≤ 3x - 7, the line you draw should be dashed to indicate that points on the line are not included in the solution set. Finally, shade the area below the line because the inequality is less than (<), which means the solution includes all the points below the line.