Examine the graph of $f(x) = 0.5x - 2$ at right.

1. Calculate the area of the shaded region using geometry. (Recall that area below the $x$-axis is considered negative.)

   Hint (a):

   Find the area of each triangle separately. Recall that the area below the $x$-axis is negative. Add the negative and the positive regions together.

   Answer (a):

   $-1\frac{3}{4}$

   More Help (a):

   $\text{[Area of triangle A]} + \text{[Area of triangle B]}$

   $\frac{1}{2}(4)(f(0))+\frac{1}{2}(7-4)(f(7))$

   $\frac{1}{2}(4)(-2)+\frac{1}{2}(3)(1.5)=$

2. What is the value of $k$ if the area under the curve for $0 ≤ x ≤ k$ is $10$? How did you obtain your solution?

   Hint 1(b):

   $\text{[Area of triangle A]} + \text{[Area of triangle B]} = 10$

   Hint 2(b):

   $\frac{1}{2}(4)(f(0))+\frac{1}{2}(k-4)(f(k))=10$

   Hint 3(b):

   $\frac{1}{2}(4)(f(0))+\frac{1}{2}((0.5x-2)-4)(0.5x-2)=10$

   Hint 4(b):

   Simplify, and solve for $k$.