To create a non-proportional linear relation with a slope of 3, use the equation y = 3x + 9, which has a y-intercept of 9. This ensures the graph will not pass through the origin and depicts a non-proportional relationship, with the slope indicating a rise of 3 on the y-axis for every increase of 1 on the x-axis.
To create a graph that is a linear relation with a slope of 3 that is NOT a proportional relationship, you can use the linear equation format y = mx + b, where m is the slope and b is the y-intercept. Since a proportional relationship means the line goes through the origin (0,0), to create a non-proportional relationship, we make sure that the y-intercept is not zero. In this case, use b = 9. So the equation of the line will be y = 3x + 9.
This line will have a slope of 3, which means for every increase of 1 in the x-value, the y-value will increase by 3. Graphically, you would plot the y-intercept at (0, 9) on the vertical axis. From this point, you would rise 3 units on the vertical axis for every 1 unit you move to the right on the horizontal axis. Below is the attached graph.