Question

If a graph is proportional what characteristic does it display?

Answer 1

A graph is proportional if it displays a linear relationship that passes through the origin (0,0). This means that as one variable changes, the other variable changes at a constant rate. In practical terms, a proportional graph shows that for every increase in one variable, there is a corresponding constant increase in the other variable, which indicates a constant ratio between the two. The key characteristics include:

1. **Straight Line**: The graph is a straight line.
2. **Passes through the Origin**: The line passes through the point (0,0).
3. **Constant Ratio**: The ratio of the two variables remains constant, meaning that if you take any two points on the line, the ratio of their y-values to their x-values will be the same.

This indicates that if the relationship described by the graph is expressed in an equation, it would typically take the form \( y = kx \), where \( k \) is a constant (the constant of proportionality).