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 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, we need to find the area of the rectangle formed by the given boundaries.
Step 1: Draw a coordinate plane and plot the given boundaries: x = 4, y = 2, y = 8, and the y-axis.
Step 2: Identify the coordinates of the points where the boundaries intersect.
- The x = 4 boundary intersects with the y-axis at (4, 0).
- The y = 2 boundary intersects with the x-axis at (0, 2).
- The y = 8 boundary intersects with the x-axis at (0, 8).
Step 3: Determine the length of the sides of the rectangle.
- The length of the rectangle is the difference between the y-coordinates of the intersection points of y = 2 and y = 8, which is 8 - 2 = 6 units.
- The width of the rectangle is the x-coordinate of the intersection point of x = 4 and the x-axis, which is 4 units.
Step 4: Calculate the area of the rectangle.
- The area of a rectangle is found by multiplying its length by its width.
- In this case, the area is 6 units (length) * 4 units (width) = 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.