Final answer:
The question entails sketching the region enclosed by the lines y = 2x, y = 8x, and y = 18x in the first quadrant (x > 0). Draw each line with increasing slopes, starting from the origin and shade the pie-slice-shaped region between them.
Step-by-step explanation:
The student has asked to sketch the region enclosed by the curves y = 2x, y = 8x, and y = 18x, with the condition that x > 0. To sketch this, we start by plotting each linear equation on the same graph, with x on the horizontal axis and y on the vertical axis. Since all these equations are linear and directly proportional, they will form a set of lines that pass through the origin (0,0).
First, draw the line y = 2x, which will be the line with the shallowest slope. Next, draw the line y = 8x, which will have a steeper slope, and finally, draw the line y = 18x, which will have the steepest slope among the three. The region enclosed by these lines is the area between them above the x-axis (x > 0). This region will look like a wedge or a slice of pie, with the point of the slice located at the origin.
To differentiate between these lines, you could label each one and color in the region that is enclosed for clearer visualization.