what 2 things must a graph do to be a proportional reationship
A graph must have the following two characteristics in order for it to represent a proportional relationship:
1. It must be a straight line: In a proportional relationship, the graph must be a straight line that passes through the origin (0,0) on the coordinate plane.
2. It must have a constant slope: The slope of the line represents the rate of change between the two variables in the relationship. In a proportional relationship, the slope is constant, meaning that it remains the same for all values of x and y.
To be a proportional relationship, a graph must fulfill two conditions:
1. Passes through the origin: The graph must contain the point (0,0), which is the origin of the coordinate plane. This means that when one variable is zero, the other variable must also be zero.
2. Forms a straight line: The graph should be a straight line that doesn't curve or bend. Any increase in one variable should result in a constant, proportional increase in the other variable. This indicates a direct, linear relationship between the two variables.
To determine whether a graph represents a proportional relationship, there are two key things to look for:
1. Passes through the origin: A proportional relationship implies that when one variable is zero, the other variable must also be zero. Therefore, if the graph passes through the point (0,0) or the origin on the coordinate plane, it suggests a proportional relationship.
2. Maintains a straight line: In a proportional relationship, the ratio between the two variables remains constant. As a result, the graph of such a relationship will always be a straight line that does not curve or bend.
By confirming that a graph passes through the origin and remains a straight line, you can determine whether it represents a proportional relationship.