Calculate the gradient (slope) of the line.

The given points are $(x_1, y_1) = (-4, 0)$ and $(x_2, y_2) = (8, 9)$.
The formula for the gradient $m$ is:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Substitute the coordinates:

$$m = \frac{9 - 0}{8 - (-4)}$$ $$m = \frac{9}{8 + 4}$$ $$m = \frac{9}{12}$$ $$m = \frac{3}{4}$$

Using the point $(-4, 0)$ and the gradient $m = \frac{3}{4}$:

$$y - y_1 = m(x - x_1)$$ $$y - 0 = \frac{3}{4}(x - (-4))$$ $$y = \frac{3}{4}(x + 4)$$

Multiply both sides by 4 to eliminate the fraction:

$$4y = 3(x + 4)$$ $$4y = 3x + 12$$

Rearrange the equation $4y = 3x + 12$ to have the constant term on one side:

$$3x - 4y = -12$$

To get 1 on the right side, divide the entire equation by -12:

$$\frac{3x}{-12} - \frac{4y}{-12} = \frac{-12}{-12}$$

Simplify the fractions:

$$\frac{x}{-4} + \frac{y}{3} = 1$$

Comparing this to $\frac{x}{a} + \frac{y}{b} = 1$, we have $a = -4$ and $b = 3$.