a) Describe how you know that a graph is proportional.
b) Describe how you know an equation is proportional. Give an example of an equation that is proportional and a graph that is not proportional.
c) Describe how you know that a table is proportional.
Math
a) A graph is proportional if it represents a direct variation or a linear relationship between two variables. This means that as one variable increases, the other variable also increases or decreases at a constant rate. In a proportional graph, the points will lie on a straight line that passes through the origin (0,0) and is not curved or angled.
b) An equation is proportional if it can be expressed in the form y = kx, where y and x are variables and k is a constant. In a proportional equation, as x increases, y also increases or decreases at a constant rate determined by the value of k. An example of a proportional equation is y = 2x, where y is directly proportional to x with a constant of proportionality equal to 2. On the other hand, an equation that is not proportional could be y = x^2, where y is not directly proportional to x and the graph would form a curve.
c) A table is proportional if the ratio between each pair of corresponding values in the table is constant. In a proportional table, as one value increases or decreases, the other value also increases or decreases at a constant rate. The values in a proportional table would have a constant ratio. For example, consider the table:
x | y
--------
1 | 2
2 | 4
3 | 6
In this table, the ratio of y to x is always 2:1, indicating that y is directly proportional to x with a constant ratio of 2. Therefore, the table is proportional.