1. The problem is to find the gradient of a line given by the equation $ax + by + c = 0$. 2. The formula to find the gradient $m$ of a line in the form $ax + by + c = 0$ is: $$m = -\frac{a}{b}$$ This comes from rearranging the equation into slope-intercept form $y = mx + c$. 3. To find the gradient, isolate $y$: $$ax + by + c = 0$$ $$by = -ax - c$$ $$y = -\frac{a}{b}x - \frac{c}{b}$$ 4. From this, the coefficient of $x$ is the gradient $m = -\frac{a}{b}$. 5. Example: For the line $x + 3y - 4 = 0$, $a=1$, $b=3$, so $$m = -\frac{1}{3}$$ 6. Therefore, the gradient of the line $x + 3y - 4 = 0$ is $-\frac{1}{3}$.