Given the following graph, determine whether the rate of change is uniform or not111222333444555666111222333000

The graph does not represents a function

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

Q: How can I tell if a rate of change is uniform just by looking?

Look for a straight line! If the graph forms a perfect straight line, the rate of change is uniform. If it's curved, bent, or has different slopes in different sections, it's non-uniform.

Q: What if the line goes down instead of up?

The direction doesn't matter for uniformity! A decreasing straight line still has uniform rate of change - it's just negative. The key is that it's straight.

Q: What does 'rate of change' actually mean?

Rate of change shows how much y changes for each unit of x. Think of it like speed: uniform rate means constant speed, while non-uniform means changing speed.

Q: Can I use any two points on the line?

Yes! For a straight line, the slope between any two points will be identical. This is what makes the rate of change uniform.

Rate of Change with Linear Graph 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

00:06 First, we ask, is the rate of change uniform?

00:11 Let's pick some points on the graph and have a look.

00:18 Notice how the change between each pair of points stays the same.

00:46 That means the graph shows a uniform rate of change.

00:49 And there you go, that's the solution to our 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 solve this problem, let's analyze the graph of the line:

Step 1: Identify two points on the line. For simplicity, let's choose the intercept at $x = 1$ and $y = 3$ , and another at $x = 6$ and $y = 0$ (assuming these are easily readable points).
Step 2: Calculate the slope using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ .
Step 3: Substituting in our chosen points, the slope is $\frac{0 - 3}{6 - 1} = \frac{-3}{5}$ .
Step 4: Since the graph is a straight line and the slope is constant, the rate of change is uniform.

Therefore, the graph shows a constant or uniform rate of change.

The solution to the problem is thus Uniform.

Since the correct answer is shown in the multiple-choice option "Uniform", we conclude it matches the analysis result.

Final Answer

Uniform

Key Points to Remember

Essential concepts to master this topic

Linear Graph Rule: Straight lines have constant rate of change
Slope Calculation: Use $\frac{y_2 - y_1}{x_2 - x_1}$ between any two points
Verification: Calculate slope between different point pairs: should be identical ✓

Common Mistakes

Avoid these frequent errors

Assuming all graphs have uniform rates
Don't automatically assume uniform rate without checking the graph shape! Curved lines have non-uniform rates even if they look smooth. Always confirm the graph is a straight line before concluding uniform rate of change.

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

How can I tell if a rate of change is uniform just by looking?

Look for a straight line! If the graph forms a perfect straight line, the rate of change is uniform. If it's curved, bent, or has different slopes in different sections, it's non-uniform.

What if the line goes down instead of up?

The direction doesn't matter for uniformity! A decreasing straight line still has uniform rate of change - it's just negative. The key is that it's straight.

Do I need to calculate the exact slope value?

Not necessarily for determining uniformity! You just need to confirm it's a straight line. However, calculating slope helps verify your visual assessment.

What does 'rate of change' actually mean?

Rate of change shows how much y changes for each unit of x. Think of it like speed: uniform rate means constant speed, while non-uniform means changing speed.

Can I use any two points on the line?

Yes! For a straight line, the slope between any two points will be identical. This is what makes the rate of change uniform.

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