Analyzing Rate of Change: Uniform or Non-Uniform from X-Y Coordinate Table

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

A uniform rate of change means the function increases or decreases by the same amount for every equal change in x. This creates a straight line graph with constant slope.

Q: Do I need to check all consecutive pairs or just the first and last?

You must check all consecutive pairs! Rate of change can vary between different intervals. In this problem, the first slope (-0.2) differs from the others (-0.4).

Q: What if I get the same slope for some pairs but not others?

Then the rate is non-uniform! Even if most slopes match, just one different slope means the rate changes across the function's domain.

Q: How do I remember the slope formula?

Think "rise over run" - how much the function rises (or falls) divided by how much it runs horizontally. Always $ \frac{y_2 - y_1}{x_2 - x_1} $!

Q: Can a function have uniform rate of change in some parts but not others?

No! We're analyzing the entire function shown in the table. If any consecutive slopes differ, the overall rate of change is non-uniform for this function.

Rate of Change with Consecutive Point Comparisons

Given a table showing points on the graph of a function, determine whether or not the rate of change is uniform.

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Step-by-step video solution

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00:00 Determine if the rate of change is uniform?

00:06 It appears that the change in X values is always equal

00:13 However, the change in Y values is not equal

00:16 Therefore, the rate of change is not uniform

00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given a table showing points on the graph of a function, determine whether or not the rate of change is uniform.

Step-by-step solution

To determine whether the rate of change is uniform, we calculate the slope between each consecutive pair of points provided in the table:

Calculate the slope between $(-5, 3)$ and $(0, 2)$ :
- The change in $Y$ is $2 - 3 = -1$ .
- The change in $X$ is $0 - (-5) = 5$ .
- Thus, the slope is $\frac{-1}{5} = -0.2$ .
Calculate the slope between $(0, 2)$ and $(5, 0)$ :
- The change in $Y$ is $0 - 2 = -2$ .
- The change in $X$ is $5 - 0 = 5$ .
- Thus, the slope is $\frac{-2}{5} = -0.4$ .
Calculate the slope between $(5, 0)$ and $(10, -2)$ :
- The change in $Y$ is $-2 - 0 = -2$ .
- The change in $X$ is $10 - 5 = 5$ .
- Thus, the slope is $\frac{-2}{5} = -0.4$ .

We observe that the slopes are not all the same: the first slope $-0.2$ differs from the others, which are both $-0.4$ . Therefore, the rate of change is not uniform across the intervals.

Thus, the rate of change in the function represented by the table is non-uniform.

Final Answer

Non-uniform

Key Points to Remember

Essential concepts to master this topic

Rule: Calculate slope between each consecutive pair of points
Technique: Use $\frac{\Delta y}{\Delta x}$ formula: $\frac{-1}{5} = -0.2$ for first interval
Check: Compare all slopes: if any differ, rate is non-uniform ✓

Common Mistakes

Avoid these frequent errors

Calculating slope incorrectly or skipping intervals
Don't calculate $\frac{\Delta x}{\Delta y}$ or only check some pairs = wrong conclusion! This reverses the slope formula or misses changing rates. Always use $\frac{\Delta y}{\Delta x}$ and check every consecutive pair of points.

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?

A uniform rate of change means the function increases or decreases by the same amount for every equal change in x. This creates a straight line graph with constant slope.

Do I need to check all consecutive pairs or just the first and last?

You must check all consecutive pairs! Rate of change can vary between different intervals. In this problem, the first slope (-0.2) differs from the others (-0.4).

What if I get the same slope for some pairs but not others?

Then the rate is non-uniform! Even if most slopes match, just one different slope means the rate changes across the function's domain.

How do I remember the slope formula?

Think "rise over run" - how much the function rises (or falls) divided by how much it runs horizontally. Always $\frac{y_2 - y_1}{x_2 - x_1}$ !

Can a function have uniform rate of change in some parts but not others?

No! We're analyzing the entire function shown in the table. If any consecutive slopes differ, the overall rate of change is non-uniform for this function.

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