Graphing on a Varied Scale

What is a proportional situation?

• A proportional situation is one in which two quantities are unrelated and have no relationship.

• A proportional situation is one in which two quantities are related in such a way that they maintain a constant ratio or proportion.

Answer explanation

The question asks about a proportional situation. The correct answer is that a proportional situation is one where two quantities maintain a constant ratio or proportion. This means that as one quantity increases or decreases, the other does so in a way that their ratio remains the same. The other option, stating that the quantities are unrelated, is incorrect as it contradicts the definition of proportionality.

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How can you identify a proportional situation in a graph?

• The graph will show a straight line passing through the origin.

• The graph will show a curved line passing through the origin.

Answer explanation

In a proportional situation, the graph will always show a straight line passing through the origin. This is because the ratio between the two variables remains constant throughout, which is represented by a straight line. The other option of a curved line is incorrect as it represents a non-proportional relationship.

What does it mean for a graph to have a varied scale?

• The intervals or units on the graph's axes are not consistent or equal.

• The graph has multiple axes.

Answer explanation

A graph with a varied scale means that the intervals or units on the graph's axes are not consistent or equal. This is the correct answer because it directly addresses the question about what it means for a graph to have a varied scale. The other option, which suggests that the graph has multiple axes, does not necessarily imply a varied scale.

Explain how to graph a proportional situation on a varied scale.

• Use a fixed scale for both axes.

• Adjust the scale of the axes to accurately represent the relationship between the variables.

Answer explanation

To graph a proportional situation on a varied scale, it's important to adjust the scale of the axes. This is because the scale adjustment allows for an accurate representation of the relationship between the variables. Using a fixed scale for both axes wouldn't provide the flexibility needed for varied scales.

In a proportional situation, what does the slope of the graph represent?

• Y-intercept

• Rate of change or constant of proportionality

Answer explanation

In a proportional situation, the slope of the graph represents the rate of change or the constant of proportionality. This means that for every unit increase in the x-axis, the y-axis increases by a constant amount. This constant amount is the slope of the graph, which is the rate of change or constant of proportionality in this context.

What are some examples of proportional situations in real life?

• Weight and height in a growing child

• Distance and time in a constant speed journey

Answer explanation

The correct answer is 'Distance and time in a constant speed journey'. This is a proportional situation in real life because the distance covered is directly proportional to the time spent traveling. The longer the journey time, the greater the distance covered, assuming the speed remains constant. This is a fundamental principle of motion.

How can you determine the scale of a graph?

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What are the advantages of using a varied scale in graphing?

• Better representation and accurate comparisons

• Improved visualization and understanding

Answer explanation

Using a varied scale in graphing offers better representation and accurate comparisons. It allows for a more precise visualization of data points, making it easier to identify trends and patterns. This, in turn, leads to a more effective analysis and interpretation of the data being presented.

What are the disadvantages of using a varied scale in graphing?

• Improving data accuracy, making it easier to compare values, and providing clear information to the audience.

• Distorting the data, difficult to compare values accurately, and misleading the audience.

Answer explanation

The disadvantages of using a varied scale in graphing include distorting the data, making it difficult to compare values accurately, and potentially misleading the audience. A varied scale can create a false impression of the data's trends and relationships, leading to incorrect interpretations.

Explain how to interpret a graph with a varied scale.

• Carefully analyze the axes, units, tick marks, and annotations to understand the scale and interpret the data accurately.

• Use the same scale for all variables on the graph.

Answer explanation

To interpret a graph with a varied scale, it is essential to carefully analyze the axes, units, tick marks, and annotations. This helps in understanding the scale and interpreting the data accurately. Using the same scale for all variables on the graph is not the correct approach, as it may lead to misinterpretation of the data.