Final answer:
To find the area enclosed by the graphs of y = 8 - 3x, y = 6 - x, and y = 3, we must first determine the points of intersection to identify the vertices of the region. After sketching these lines on a graph and shading the enclosed area, we use geometric formulas to calculate the total area.
Step-by-step explanation:
To find the area of the region enclosed by the graphs of y = 8 - 3x, y = 6 - x, and y = 3, we need to follow a few steps. First, we determine the points of intersection by setting the equations equal to each other. This gives us the vertices of the enclosed region. Next, we sketch the three lines on the same graph to visualize the region.
Now, to find the points of intersection, we'll set the equations equal to one another in pairs:
- For the intersection of y = 8 - 3x and y = 6 - x, we set 8 - 3x = 6 - x.
- For the intersection of y = 6 - x and y = 3, we set 6 - x = 3.
- For the intersection of y = 8 - 3x and y = 3, we set 8 - 3x = 3.
Once the vertices are found, we draw the lines and shaded the enclosed area on the graph. We then use the formula for the area of triangles and other geometric shapes if necessary to find the total area enclosed by these lines.