Final answer:
To graph the inequality y < x + 4, one must draw a dashed boundary line at y = x + 4, label the line as f(x), choose an appropriate scale for the axes, and shade the area under the line to show the solution set where the inequality is true.
Step-by-step explanation:
To graph the inequality y < x + 4, we start by graphing the line y = x + 4. This line will serve as the boundary for the inequality. To draw this line, we can plot two points where the equation is true, for instance (0, 4) and (-4, 0), and then draw a straight line through them. Since the inequality is y < x + 4, the area below this line is the solution set. We use a dashed line to indicate that the points on the line are not included in the solution.
To correctly label the graph, we write f(x) = x + 4 next to the line. For the axes, we can use a scale that includes the line correctly; if f(x) = 10,0, then we scale the y-axis up to 10 and 0≤x≤20 for the x-axis. After drawing and labeling the axes, we can shade the region that represents the solution to the inequality, which is the area below the dashed line.
The graphical representation of dependencies of y on x and the solutions to inequalities provides a visual understanding of these mathematical concepts. Graphing is an effective tool in representing data and solving equations and inequalities in a visual and easy-to-understand manner.