Question

what are the main characteristics of a proportional relationship between two variables?
they are linear (straight line) and also pass through the origin.
the x to y ratio is a constant of proportionality.
they pass through the origin.
they are curved

Explanation:

A proportional relationship between two variables follows the form $y = kx$ where $k$ is the constant of proportionality. This means:

1. The relationship is linear (forms a straight line) and passes through the origin $(0,0)$, since when $x=0$, $y=0$.
2. The ratio $\frac{y}{x}$ (or $\frac{x}{y}$ as a reciprocal constant) is always equal to the constant $k$, so this ratio is constant.
3. Curved relationships do not represent proportionality, as they do not follow the linear $y=kx$ form.

Answer:

• They are linear (straight line) and also pass through the origin.
• The x to y ratio is a constant of proportionality.
• They pass through the origin.