Draw graphs of the lines passing through the given points and determine the angle between each pair of lines.

Mstari wa kwanza unapita kwenye pointi $(-1, 1)$ na $(3, 2)$.
Kanuni ya mteremko $m = \frac{y_2 - y_1}{x_2 - x_1}$.

$$m_1 = \frac{2 - 1}{3 - (-1)} = \frac{1}{3 + 1} = \frac{1}{4}$$

Mteremko wa mstari wa kwanza ni $\frac{1}{4}$.

Mstari wa pili unapita kwenye pointi $(2, -2)$ na $(0, m)$.

$$m_2 = \frac{m - (-2)}{0 - 2} = \frac{m + 2}{-2}$$

Mteremko wa mstari wa pili ni $\frac{m + 2}{-2}$.

Kwa kuwa mistari hiyo miwili ni wima, bidhaa ya miteremko yao ni $-1$.

$$m_1 \cdot m_2 = -1$$ $$\frac{1}{4} \cdot \frac{m + 2}{-2} = -1$$

$$\frac{m + 2}{-8} = -1$$

Panua pande zote mbili kwa $-8$:

$$m + 2 = (-1) \times (-8)$$ $$m + 2 = 8$$

Toa 2 kutoka pande zote mbili:

$$m = 8 - 2$$ $$m = 6$$

Thamani ya $m$ ni $\boxed{\text{6}}$.