When we plot a graph between volume (V) and the inverse of pressure (1/P) for an ideal gas at constant temperature, the curve obtained is a straight line. This relationship is known as Boyle`s law. Boyle`s law states that the product of pressure and volume is constant for a fixed amount of gas at a constant temperature. Mathematically, it can be written as P × V = constant.
When we rearrange this equation to isolate volume, we get V = constant / P. This equation represents a hyperbola since the product of pressure and volume is constant. However, if we plot the graph between V and 1/P, the equation becomes V = constant × 1/P, which simplifies to V = constant × (1/P). This equation represents a straight line when plotted on a graph.
Therefore, the correct answer is option 1: a straight line.