Sketch the region enclosed by the lines x = 0, x = 6, y = 2, and y = 6.
6. Find the area of the region.
To sketch the region, draw a rectangle with vertices at (0,2), (6,2), (6,6), and (0,6). This region is enclosed by the lines x=0, x=6, y=2, and y=6.
To find the area of this region, we can use the formula for the area of a rectangle:
Area = base x height
The base of the rectangle is the distance between x=0 and x=6, which is 6. The height of the rectangle is the distance between y=2 and y=6, which is 4. Therefore, the area of the region is:
Area = 6 x 4 = 24
So the area of the region enclosed by the lines x=0, x=6, y=2, and y=6 is 24 square units.
To sketch the region enclosed by the lines x = 0, x = 6, y = 2, and y = 6, follow these steps:
1. Draw a rectangular coordinate system on a piece of graph paper.
2. Label the x-axis and y-axis.
3. Draw a vertical line at x = 0 and label it as such.
4. Draw another vertical line at x = 6 and label it as such.
5. Draw a horizontal line at y = 2 and label it as such.
6. Draw another horizontal line at y = 6 and label it as such.
7. Shade in the region between the lines x = 0 and x = 6, and between the lines y = 2 and y = 6.
To find the area of the region, we can calculate the area of the rectangle that is formed by the intersection of the lines x = 0, x = 6, y = 2, and y = 6.
The length of the rectangle is 6 units (the distance between x = 0 and x = 6).
The width of the rectangle is 4 units (the distance between y = 2 and y = 6).
To find the area of a rectangle, multiply the length by the width:
Area = Length × Width
Area = 6 units × 4 units
Area = 24 square units
Therefore, the area of the region enclosed by the lines x = 0, x = 6, y = 2, and y = 6 is 24 square units.