What 2 things must a graph do to be a proportional relationship?

Answer 1

For a graph to represent a proportional relationship, it must meet two key criteria:

1. Linear Relationship through the Origin: The graph must be a straight line that passes through the origin (0,0). This indicates that when one variable is zero, the other variable is also zero, reflecting the concept of direct proportionality.

2. Constant Rate of Change: The slope of the line must be constant. This means that the ratio of the two variables remains the same regardless of the values of the variables. In other words, for any two points on the line, the ratio of the change in the y-coordinate to the change in the x-coordinate (rise/run) should be consistent.

These two criteria ensure that the relationship between the variables being graphed is proportional.