Question

the equation y equals 1/5x represents a proportional relationship. explain how you can tell the relationship is proportional from the graph of the equation, and how can you find the constant of proportionality

Answer 1

If the equation is in y = k*x form, then we have a direct proportional relationship between x and y. In this case, y = (1/5)*x is in the form y = k*x where k = 1/5. So this equation is proportional. The constant of proportionality is k = 1/5

In terms of a graph, you can tell if it has the following properties:
1) The graph goes through the origin (0,0) which is where the x and y axis cross
2) The graph is a straight line

You should find that graphing y = (1/5)x will satisfy both properties above, so that will visually confirm you have the right answer. The graph is shown in the attached image. The red line represents the graph of the equation. The red line goes through (0,0) and (5,1), which are point A and point B respectively.