Given the following graph, determine whether the rate of change is uniform or not–3–3–3–2–2–2–1–1–1111222333444–1–1–1111222333000

The graph does not represents a function

Graph Analysis: Determining Uniform vs Non-uniform Rate of Change in Linear Functions

Q: How can I tell if a line is perfectly straight on a graph?

Look carefully at the entire line from start to finish. A straight line has no curves, bends, or changes in direction. You can also check by calculating the slope between different pairs of points - they should all be equal!

Q: What does uniform rate of change actually mean?

Uniform rate of change means the function increases or decreases by the same amount for every unit change in x. It's like climbing stairs - each step up is the same height!

Q: Can I have uniform rate of change if the line goes down?

Absolutely! A downward sloping straight line has uniform rate of change too. The rate is just negative, meaning y decreases by a constant amount as x increases.

Q: What if the graph looks almost straight but has tiny curves?

If there are any curves, no matter how small, the rate of change is non-uniform. Even slight curves mean the slope changes, so the rate isn't constant throughout the function.

Q: How do I calculate the actual rate of change?

Pick any two clear points on the line and use the slope formula: $ m = \frac{y_2 - y_1}{x_2 - x_1} $. This gives you the constant rate for the entire linear function!

Linear Functions with Rate of Change Analysis

Given the following graph, determine whether the rate of change is uniform or not

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Is the function changing at a constant rate?

00:09 Let's check if the differences in the X and Y values stay the same.

00:22 Now, let's calculate these differences step by step.

00:32 The differences are equal, so the rate of change is constant.

00:37 And that's how we solve this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the following graph, determine whether the rate of change is uniform or not

Step-by-step solution

To determine if the rate of change in the given graph is uniform, we need to analyze the graph and check if it is a straight line.

Step 1: Check for linearity - The most direct way to determine if the graph has a uniform rate of change is by inspecting it for linearity, which means the graph forms a straight line.

Step 2: Analyze the path - The given SVG code and description imply a straight diagonal line, suggesting a constant slope.

For a linear function, the slope $m = \frac{y_2 - y_1}{x_2 - x_1}$ is constant throughout. As the graph is described as a straight line, any change in $x$ results in a proportional change in $y$ , confirming the slope does not vary.

Consequently, the graph displays a uniform rate of change. Therefore, the solution to this problem is uniform.

Final Answer

Uniform

Key Points to Remember

Essential concepts to master this topic

Linearity Test: A straight line graph indicates uniform rate of change
Slope Formula: Calculate $m = \frac{y_2 - y_1}{x_2 - x_1}$ between any two points
Verification: Check that slope remains constant between different point pairs ✓

Common Mistakes

Avoid these frequent errors

Confusing curved lines with straight lines
Don't assume any slanted line is straight without careful inspection = wrong rate determination! A slightly curved line has non-uniform rate of change even if it looks mostly straight. Always verify the graph forms a perfectly straight line by checking multiple segments.

Practice Quiz

Test your knowledge with interactive questions

Look at the graph below and determine whether the function's rate of change is constant or not:

FAQ

Everything you need to know about this question

How can I tell if a line is perfectly straight on a graph?

Look carefully at the entire line from start to finish. A straight line has no curves, bends, or changes in direction. You can also check by calculating the slope between different pairs of points - they should all be equal!

What does uniform rate of change actually mean?

Uniform rate of change means the function increases or decreases by the same amount for every unit change in x. It's like climbing stairs - each step up is the same height!

Can I have uniform rate of change if the line goes down?

Absolutely! A downward sloping straight line has uniform rate of change too. The rate is just negative, meaning y decreases by a constant amount as x increases.

What if the graph looks almost straight but has tiny curves?

If there are any curves, no matter how small, the rate of change is non-uniform. Even slight curves mean the slope changes, so the rate isn't constant throughout the function.

How do I calculate the actual rate of change?

Pick any two clear points on the line and use the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ . This gives you the constant rate for the entire linear function!

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