Describe how you know that a graph is proportional.
A graph is proportional when it represents a direct relationship between two variables, where an increase in one variable results in a corresponding increase in the other variable, or a decrease in one variable results in a corresponding decrease in the other variable. This means that the ratio of the dependent variable to the independent variable remains constant throughout the graph.
To determine if a graph is proportional, one can look for some key characteristics:
1. Straight line: A proportional graph typically shows a straight line when the values of the two variables are plotted on a Cartesian coordinate system. The line should pass through the origin (0,0), indicating that when both variables are zero, they have a direct relationship.
2. Constant ratio: The slope of the line in a proportional graph represents the constant ratio between the two variables. If the slope is positive, it means that an increase in the independent variable corresponds to an increase in the dependent variable, and vice versa. If the slope is negative, it indicates that an increase in one variable leads to a decrease in the other variable.
3. Scatterplot clustering: In a proportional graph, the points plotted on the graph tend to cluster around the line. The closer the points are to the line, the stronger the indication of proportionality.
4. Division of one variable by the other: Another way to check for proportionality is by dividing the values of one variable by the corresponding values of the other variable. If the resulting numbers are constant, it confirms that the graph is proportional.
Overall, to determine proportionality, one must examine the linearity, constant ratio, clustering of points, and the division of variables in the graph. If these characteristics are present, then it can be concluded that the graph represents a proportional relationship between the variables.