Chapter F - Foundations: A Prelude to Functions - Section F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry - F.2 Assess Your Understanding - Page 18: 73

$b=13$

If a point is on the graph, the $(x,y)$ coordinates satisfy the equation. Here, $(3,b)$ is on th graph, therefore we should plug in these coordinates into the given equation to obtain: $y=4x+1$ $b=4(3)+1$ $b=13$ The point $(3,13)$ is on the graph so $b=13$.