Draw and label the axes. The x-axis should represent Temperature (^ C) and the y-axis should represent Solubility (g/100g of water).

The x-axis should represent Temperature ($^\circ \text{C}$) and the y-axis should represent Solubility (g/100g of water).

• For the x-axis (Temperature): A suitable scale would be $1 \text{ cm}$ (or 1 major grid square) representing $10^\circ \text{C}$. This allows the temperature range from $10^\circ \text{C}$ to $100^\circ \text{C}$ to fit well.
• For the y-axis (Solubility): A suitable scale would be $1 \text{ cm}$ (or 1 major grid square) representing $10 \text{ g/100g of water}$. Start the y-axis at a value like $70 \text{ g/100g of water}$ to accommodate the lowest solubility value of $80 \text{ g/100g of water}$.

For example, plot $(10, 80)$, $(20, 88)$, $(30, 96)$, and so on, up to $(100, 180)$.

This curve represents the solubility curve for potassium nitrate.

Based on interpolation between $60^\circ \text{C}$ (124 g/100g water) and $70^\circ \text{C}$ (136 g/100g water):

The solubility of potassium nitrate at $65^\circ \text{C}$ is $\boxed{\text{130 g/100g of water}}$.

Based on interpolation between $80^\circ \text{C}$ (148 g/100g water) and $90^\circ \text{C}$ (162 g/100g water):

This means $150.8 \text{ g}$ of potassium nitrate dissolves in $100 \text{ g}$ of water at $82^\circ \text{C}$.

Since $50 \text{ g}$ of water is half of $100 \text{ g}$ of water, the mass of potassium nitrate that dissolves will also be half.

The mass of potassium nitrate that would dissolve in $50 \text{g}$ of water at $82^\circ \text{C}$ is $\boxed{\text{75.4 g}}$.