Find the number of square units in the area of the region in the first quadrant which is bounded by x = 4, the y-axis, y = 2, and y = 8.
To find the area of the region described, we need to calculate the area of the rectangle formed by the lines x = 4, the y-axis, y = 2, and y = 8.
Step 1: Draw a diagram of the region described.
- Draw the x-axis and y-axis.
- Plot the point (4, 0) on the x-axis.
- Draw the line x = 4, passing through the point (4, 0).
- Plot the point (0, 2) on the y-axis.
- Draw the line y = 2, passing through the point (0, 2).
- Plot the point (0, 8) on the y-axis.
- Draw the line y = 8, passing through the point (0, 8).
- Finally, draw the rectangle formed by these lines.
Step 2: Calculate the length and width of the rectangle.
- The length of the rectangle is the distance between the lines x = 4 and the y-axis. Since the line x = 4 is vertical, the length is the distance between the point (4, 0) and the y-axis, which is 4 units.
- The width of the rectangle is the distance between the lines y = 2 and y = 8. Since these lines are horizontal, the width is the distance between the points (0, 2) and (0, 8) on the y-axis, which is 8 - 2 = 6 units.
Step 3: Calculate the area of the rectangle.
- The area of a rectangle is given by the formula: Area = length × width.
- Substituting the values we found: Area = 4 units × 6 units = 24 square units.
Therefore, the number of square units in the area of the region in the first quadrant bounded by x = 4, the y-axis, y = 2, and y = 8 is 24 square units.