Question

Show a proportional graph and equation and compare to a non proportional graph and equation.

Answer 1

Sure! Let's start by showing a proportional graph and equation.

Proportional graph:
Consider a simple linear equation y = 2x, where x represents the independent variable and y represents the dependent variable. This equation represents a proportional relationship between x and y.

The corresponding graph of this equation will be a straight line that passes through the origin (0, 0) and has a slope of 2. Each increase in x by 1 unit will result in an increase in y by 2 units.

Here is the graph of y = 2x:
```
|
|
| * <-- Line passes through (0, 0)
| \
| \
| \
|_______\_____
0
```

As you can see, the graph is a straight line that has a steady slope of 2. Also, for each increase in x by 1 unit, y increases by 2 units. This relationship remains constant throughout the graph.

Now let's compare it to a non-proportional graph and equation.

Non-proportional graph:
Consider a quadratic equation y = x^2, where x represents the independent variable and y represents the dependent variable. This equation represents a non-proportional relationship between x and y.

The corresponding graph of this equation will be a U-shaped curve known as a parabola.

Here is the graph of y = x^2:
```
.
.
.
.
.
.
.
```

As you can see, the graph is a curve rather than a straight line. Also, as x increases, y does not have a constant rate of change, unlike in the proportional graph. In a non-proportional relationship, the rate of change between x and y varies across different parts of the graph.

In summary, a proportional relationship has a constant rate of change between x and y, resulting in a straight-line graph. On the other hand, a non-proportional relationship does not have a constant rate of change and results in a curved graph, such as a parabola.