The length of the portion of the straight line 3x + 4y = 12 intercepted between the axes is:

$$\eqalign{ & 3x + 4y = 12 \cr & \Rightarrow \frac{{3x}}{{12}} + \frac{{4y}}{{12}} = 1 \cr & \Rightarrow \frac{x}{4} + \frac{y}{3} = 1 \cr & \therefore {\text{Length of intercept AB}} = \sqrt {{4^2} + {3^3}} \cr & = \sqrt {25} \cr & = 5{\text{ units}} \cr} $$