The line 2x + 7y = 28 and the two axes enclose a triangle.

Step 1. The intercepts. $y = 0$ gives $x = 14$. $x = 0$ gives $y = 4$.

Step 2. The area. $\tfrac{1}{2} \times 14 \times 4 = 28$ square units.

Step 3. The doubled line. It meets the axes at $x = 28$ and $y = 8$. The area is $\tfrac{1}{2} \times 28 \times 8 = 112$ square units.