#### Answer

Linear function for $b_{n}$ = 5n - 2

#### Work Step by Step

From graph,
If n = 1 then $b_{n}$ = 3, write this information as point form (n, $b_{n}$) = (1, 3)
If n = 2 then $b_{n}$ = 8, write this information as point form (n, $b_{n}$) = (2, 8)
Slop of the line join both points (1, 3) and (2, 8) = $\frac{8-3}{2-1}$ = 5
Equation for straight line which join both the points.
$b_{n}$ = 5 n + x
where x = constant find by put $b_{n}$ = 3 if n = 1.
3 = 5 + x
x = -2
then
$b_{n}$ = 5n - 2
Linear function for $b_{n}$ = 5n - 2