Question

Show a proportional graph and equation and compare to a non proportional graph and equation.
Proportional: y =



Non Proportional: y =

Answer 1

To illustrate a proportional graph and equation, let's consider the equation y = 2x. This equation represents a direct proportion, where y is always twice the value of x.

Here is a table of values for the proportional equation:

| x | y |
|-------|-------|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |

Now, let's plot these points on a graph:

graph(x,2x)

This graph shows a straight line that passes through the origin (0,0) and has a positive slope of 2.

For the non-proportional graph and equation, let's consider the equation y = x^2. This equation represents a non-proportional relationship, where y is not directly proportional to x.

Here is a table of values for the non-proportional equation:

| x | y |
|-------|-------|
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |

Now, let's plot these points on a graph:

graph(x,x^2)

This graph shows a curve, often referred to as a parabola. The y-values do not change at a constant rate as x increases, indicating a non-proportional relationship.

In summary, a proportional equation and graph (y = 2x) represents a direct proportion, where the ratio of y to x is constant. In contrast, a non-proportional equation and graph (y = x^2) does not have a constant ratio between y and x, representing a non-proportional relationship.