Proportional: y = 2x
Non-Proportional: y = x^2
Graph on a coordinate grid:
Proportional (y = 2x): a straight line that passes through the origin (0,0) with a slope of 2.
Non-Proportional (y = x^2): a curved line that does not pass through the origin.
Similarities: Both graphs are continuous and have a range of values for both x and y. They both increase in value as x increases.
Differences: The proportional graph is a straight line, while the non-proportional graph is a curved line. The non-proportional graph does not pass through the origin, while the proportional graph does.
To be proportional graphically means that the relationship between the x and y values can be represented by a straight line passing through the origin. To be non-proportional means that the relationship between the x and y values cannot be represented by a straight line passing through the origin.
Real-world scenario for the proportional graph (y = 2x): The relationship between the number of hours worked and the amount of money earned, if someone earns $2 for every hour worked.
Overall, the key difference between proportional and non-proportional relationships lies in the shape of the graph and whether it passes through the origin.