Consider the graph and equation, y = 3x, that represent Alonso’s walking speed. What relationship is represented by this equation and graph? What would the points (3, 9) and (5, 15) represent? Explain.
The equation y = 3x represents a linear relationship between Alonso's walking speed (y) and the distance he walks (x). It indicates that his walking speed is three times the distance he walks.
In the graph, every point on the line y = 3x represents a specific combination of distance walked (x) and walking speed (y). The x-coordinate represents the distance, while the y-coordinate represents the walking speed.
For the points (3, 9) and (5, 15), they represent specific situations for Alonso.
At point (3, 9), the x-coordinate of 3 represents the distance Alonso walked, and the y-coordinate of 9 represents his walking speed. This means that when Alonso walks a distance of 3 units (e.g., 3 meters, 3 kilometers), his walking speed is 9 (e.g., 9 meters per second, 9 kilometers per hour).
Similarly, at point (5, 15), the x-coordinate of 5 represents the distance Alonso walked, and the y-coordinate of 15 represents his walking speed. This means that when Alonso walks a distance of 5 units, his walking speed is 15.
In summary, the points (3, 9) and (5, 15) represent specific combinations of distance walked and walking speed for Alonso, according to the given equation and graph.
The equation y = 3x represents a proportional relationship. In a proportional relationship, the dependent variable (in this case, y) is directly proportional to the independent variable (x) with a constant ratio.
In this case, the equation y = 3x means that for every unit increase in x, the value of y will increase by a constant ratio of 3.
The points (3, 9) and (5, 15) represent specific data points on the graph of the equation.
For the point (3, 9), it means that when x = 3, the corresponding value of y is 9. This indicates that when Alonso walks at a speed of 3 units, he travels a distance of 9 units.
Similarly, for the point (5, 15), it means that when x = 5, the corresponding value of y is 15. This indicates that when Alonso walks at a speed of 5 units, he travels a distance of 15 units.
These points help us understand the relationship between x and y and how they are related based on the given equation. They are specific examples that show how the equation translates into real-life situations or data points.