Points A(x, y), B(3, -2) and C(4, -5) are collinear. The value of y in terms of x is ∶

Since, points A, B and C are collinear.

∴ Slope of AB = Slope of BC.

$$\begin{aligned}\Rightarrow \frac{-2 - y}{3 - x} = \frac{-5 - (-2)}{4 - 3} \\[1em] \Rightarrow \frac{-2 - y}{3 - x} = \frac{-5 + 2}{1} \\[1em] \Rightarrow \frac{-2 - y}{3 - x} = -3 \\[1em] \Rightarrow -2 - y = -3(3 - x) \\[1em] \Rightarrow -2 - y = -9 + 3x \\[1em] \Rightarrow y = -2 + 9 - 3x \\[1em] \Rightarrow y = 7 - 3x.\end{aligned}$$

Hence, Option 4 is the correct option.