Describe how you know an equation is proportional. Give an example of an equation that is proportional and a graph that is not proportional.
An equation is considered proportional when there is a constant ratio between two variables. This means that if one variable is multiplied by a certain factor, the other variable will also be multiplied by the same factor. Mathematically, if we have an equation in the form y = kx, where y and x are variables and k is a constant, the equation is proportional.
For example, let's consider the equation y = 2x. Here, if we multiply x by 2, the value of y will also be multiplied by 2. This constant ratio of 2 indicates proportionality.
On the other hand, if we have a graph that is not proportional, it implies that there is no constant ratio between the variables. For instance, consider the graph of y = x^2. Here, when we increase x by a certain amount, the increase in y is not constant. Therefore, this graph is not proportional as there is no consistent ratio between x and y.