Answer
(a) $a = \frac{1}{12}$ and $H(x) = \frac{1}{12}x$
(b) 12.5 in.
Work Step by Step
(a)
Linear function: $H(x) = ax + b$
$a = \frac{y - y_0}{x - x_0} = \frac{1 \space in.}{12 \space in.} = \frac 1 {12}$
Assuming the ramp will start at $H(x) = 0 \longrightarrow b = 0$
$$H(x) = \frac 1 {12} x $$
(b)
$$H(150) = \frac 1 {12} (150) = \frac {150} {12} = 12.5$$
