Given the following graph, determine whether the rate of change is uniform or not?–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888–3–3–3–2–2–2–1–1–1111222333444555666000

The graph does not represent a function

Analyzing Rate of Change: Determining Uniform Slope in Linear Graph

Q: What exactly does 'uniform rate of change' mean?

Uniform rate of change means the function increases or decreases by the same amount for every equal step in x. It's like walking at a steady pace - you cover the same distance every minute.

Q: How can I tell if a rate is uniform just by looking at the graph?

Look for a straight line! If the graph is perfectly straight, the rate is uniform. If it curves at all, the rate is non-uniform. It's that simple!

Q: What if the line is very steep - is the rate still uniform?

Yes! Steepness doesn't affect uniformity. A steep straight line still has uniform rate - it just means the function changes quickly but consistently.

Q: Can I calculate the actual rate of change from this graph?

Absolutely! Pick any two points on the line and use $ \text{slope} = \frac{\text{rise}}{\text{run}} $. You'll get the same answer no matter which points you choose because it's uniform!

Q: What would a non-uniform rate look like on a graph?

A curved line shows non-uniform rate. The curve means the steepness changes - sometimes increasing faster, sometimes slower. Think of a car speeding up or slowing down.

Linear Functions with Constant Rate

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 rate of change of the function constant? Let's find out!

00:10 We need to see if the differences in X and Y values stay the same.

00:15 To do this, we'll pick several points on the graph and check the rate of change.

00:49 First, let's find the differences between the X values.

00:54 The differences in X values are equal. That's a good sign!

00:58 Now, let's calculate the differences between the Y values.

01:02 The Y value differences are equal too, so the rate of change is constant!

01:07 And that's how we solve this question. Great job!

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

Remember that if the function is a straight line, its rate of change will be constant.

Due to the fact that the graph is a straight line - the rate of change is constant.

Final Answer

Uniform

Key Points to Remember

Essential concepts to master this topic

Definition: Linear functions have uniform (constant) rate of change
Visual Test: Straight line graphs always indicate uniform rate
Verification: Calculate slope between any two points - same value ✓

Common Mistakes

Avoid these frequent errors

Confusing uniform rate with steepness of line
Don't think steep lines have non-uniform rates = wrong conclusion! Steepness shows magnitude, not uniformity. Always remember that ANY straight line has uniform rate of change, regardless of how steep it appears.

Practice Quiz

Test your knowledge with interactive questions

Given the following graph, determine whether function is constant

FAQ

Everything you need to know about this question

What exactly does 'uniform rate of change' mean?

Uniform rate of change means the function increases or decreases by the same amount for every equal step in x. It's like walking at a steady pace - you cover the same distance every minute.

How can I tell if a rate is uniform just by looking at the graph?

Look for a straight line! If the graph is perfectly straight, the rate is uniform. If it curves at all, the rate is non-uniform. It's that simple!

What if the line is very steep - is the rate still uniform?

Yes! Steepness doesn't affect uniformity. A steep straight line still has uniform rate - it just means the function changes quickly but consistently.

Can I calculate the actual rate of change from this graph?

Absolutely! Pick any two points on the line and use $\text{slope} = \frac{\text{rise}}{\text{run}}$ . You'll get the same answer no matter which points you choose because it's uniform!

What would a non-uniform rate look like on a graph?

A curved line shows non-uniform rate. The curve means the steepness changes - sometimes increasing faster, sometimes slower. Think of a car speeding up or slowing down.

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