Problem 8

The given line equation is $\frac{x}{5} + \frac{y}{2} = 1$. To find the area of the triangle formed by this line and the coordinate axes, we first need to determine the points at which the line intersects the axes.

For the x-axis, we set $y=0$ and solve for $x$: $\frac{x}{5} + \frac{0}{2} = 1 \Rightarrow x = 5$. This gives us the point $(5, 0)$.

For the y-axis, we set $x=0$ and solve for $y$: $\frac{0}{5} + \frac{y}{2} = 1 \Rightarrow y = 2$. This results in the point $(0, 2)$.

Now we have a right triangle with base length 5 (along the x-axis) and height 2 (along the y-axis). The area $A$ of a right triangle can be calculated using the formula:
$$A = \frac{1}{2} \times \text{base} \times \text{height}$$

Substituting the base and height we found:
$$A = \frac{1}{2} \times 5 \times 2 = 5$$

So, the area of the triangle formed by the line $\frac{x}{5} + \frac{y}{2} = 1$ and the coordinate axes is $\boxed{5}$.

Therefore, the correct choice is B.