Show a proportional graph and equation and compare to a non proportional graph and equation.
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.
Sure!
A proportional graph is a graph where the relationship between two variables is constant. In other words, as one variable increases, the other variable also increases or decreases at a constant rate. The equation of a proportional graph takes the form y = kx, where k is a constant.
For example, let's consider the following proportional graph:
```
|
6 | .
| .
| .
3 | .
| .
| .
-------------
1 2 3
```
In this graph, as x increases by 1, y increases by 3. This is a constant rate of change. The equation for this proportional graph would be y = 3x.
Now, let's compare it to a non-proportional graph. In a non-proportional graph, the relationship between the variables is not constant. The equation does not take the form y = kx.
For example, let's consider the following non-proportional graph:
```
|
10 | .
| .
5 | .
| .
| .
-------------
1 2 3
```
In this graph, as x increases, y does not increase or decrease at a constant rate. The equation for this non-proportional graph may be something like y = x^2. As you can see, the relationship between x and y is not constant.
To summarize, a proportional graph has a constant rate of change and its equation takes the form y = kx. In contrast, a non-proportional graph does not have a constant rate of change, and its equation does not take the form y = kx.
Sure! Let's first understand what a proportional graph and equation are, and then we'll compare it with a non-proportional graph and equation.
A proportional graph is a graph that represents a proportional relationship between two quantities. In other words, as one variable increases, the other variable increases or decreases by a constant ratio. This relationship can be represented by a straight line passing through the origin (0,0) on the graph.
To create a proportional equation, you can use the formula y = kx, where y represents the dependent variable, x represents the independent variable, and k represents the constant of proportionality. The constant of proportionality, k, determines the rate at which the two variables are related.
For example, let's consider the equation y = 2x. This equation represents a proportional relationship where the constant of proportionality is 2. It means that for every increase of 1 unit in x, there will be an increase of 2 units in y. The graph of this equation would be a straight line passing through the origin (0,0).
Now, let's move on to a non-proportional graph and equation.
A non-proportional graph represents a relationship between two quantities where the ratio between them is not constant. In other words, as one variable changes, the other variable does not change by a fixed ratio.
To create a non-proportional equation, we can consider equations that involve exponents, roots, or other non-linear operations. For example, let's consider the equation y = x^2. In this equation, as x increases, y increases, but not by a constant ratio. The graph of this equation would be a curve, not a straight line.
In summary, a proportional graph and equation represents a constant ratio between two variables, while a non-proportional graph and equation do not have a constant ratio between the variables.