1. We are asked to determine the value of $b$ in the linear function $f(x) = ax + b$ given the graph information. 2. The value of $b$ in the standard form of a linear equation $f(x) = ax + b$ is the $y$-intercept, which is the point where the line crosses the $y$-axis (i.e., where $x=0$). 3. From the problem, the blue line in the top-left graph intersects the $y$-axis at $(0, -4)$. 4. Therefore, the value of $b$ is the $y$-coordinate of this intersection point, which is $-4$. 5. Hence, $b = -4$. Final answer: $b = -4$