Constant Rate of Change Practice Problems & Solutions

Master constant rate of change with step-by-step practice problems. Learn to identify linear functions, calculate slopes, and analyze graphs with instant feedback.

📚What You'll Master in This Practice Session
  • Identify constant rate of change from tables of values
  • Calculate slope from two points on a linear function
  • Recognize straight-line graphs that represent constant rates
  • Determine if a function has constant or variable rate of change
  • Interpret step graphs with constant rate patterns
  • Apply constant rate concepts to real-world scenarios

Understanding Constant Rate of Change

Complete explanation with examples

Constant Rate of Change

The meaning of the constant rate of change of a function can be seen when the variables X X change in fixed proportions and the Y Y do as well. 

For example, if the constant interval of the X X is 2 2 and also that of the Y Y is stable and does not vary from time to time.
The interval of the Y Y variables does not necessarily have to be equal to that of the X X for it to be considered a case of constant rate of change.
If the function is represented with a straight graph, it means that the rate of change is constant.
The rate of change is the slope of the function.

A constant rate of change is represented by a straight line, as seen in the following scheme:

A2 - Constant rate of change of a function

Detailed explanation

Practice Constant Rate of Change

Test your knowledge with 9 quizzes

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

XY04812-1012

Examples with solutions for Constant Rate of Change

Step-by-step solutions included
Exercise #1

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

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Step-by-Step Solution

Let's remember that if the function is not a straight line, its rate of change is not uniform.

Since the graph is not a straight line - the rate of change is not uniform.

Answer:

Non-uniform

Video Solution
Exercise #2

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

111222333444555666777888999101010111111121212131313141414151515111222333444555666777888000

Step-by-Step Solution

Let's remember that if the function is not a straight line, its rate of change is not uniform.

Since the graph is not a straight line - the rate of change is not uniform.

Answer:

Non-uniform

Video Solution
Exercise #3

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

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

Step-by-Step Solution

First we need to remember that if the function is not a straight line, its rate of change is not constant.

The rate of change is not uniform since the function is not a straight line.

Answer:

Not constant

Video Solution
Exercise #4

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

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Step-by-Step Solution

The problem requires us to determine whether the rate of change in a given graph is uniform.

A uniform rate of change corresponds to a constant slope, which is characteristic of a linear graph. First, we'll examine the graphical representation.

Upon observing the graph, we see that it displays a straight horizontal line. A horizontal line on a graph indicates that for any two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), the difference in yy-values is zero, i.e., y2−y1=0y_2 - y_1 = 0. This implies that the slope, given by the formula y2−y1x2−x1 \frac{y_2 - y_1}{x_2 - x_1} , is zero and remains constant as we move along the line.

Because the line is horizontal and does not change its slope throughout, the rate of change is indeed uniform across the entire graph.

Therefore, the rate of change is uniform.

Answer:

Uniform

Video Solution
Exercise #5

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

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.

Answer:

Uniform

Video Solution

Frequently Asked Questions

Everything you need to know about Constant Rate of Change

What is constant rate of change in simple terms?

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Constant rate of change means that as the x-variable increases by the same amount, the y-variable also changes by the same amount every time. This creates a straight line when graphed and represents the slope of a linear function.

How do you identify constant rate of change from a table?

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To identify constant rate of change from a table: 1) Calculate the change in y-values, 2) Calculate the change in x-values, 3) Divide change in y by change in x for each interval, 4) If all ratios are equal, the rate is constant.

What does a constant rate of change graph look like?

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A constant rate of change always appears as a straight line on a graph. The line can slope upward (positive rate), downward (negative rate), or remain horizontal (zero rate), but it must be perfectly straight.

Is slope the same as constant rate of change?

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Yes, slope and constant rate of change are the same concept. The slope of a linear function represents how much y changes for each unit change in x, which is exactly what constant rate of change measures.

Can a curved graph have constant rate of change?

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No, curved graphs cannot have constant rate of change. Only straight lines have constant rates because the slope must remain the same throughout the entire function for the rate to be constant.

What are real-world examples of constant rate of change?

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Common examples include: driving at steady speed (distance vs time), hourly wages (pay vs hours worked), constant temperature change, and unit pricing (total cost vs quantity purchased).

How is constant rate different from variable rate of change?

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Constant rate of change remains the same throughout the function and creates straight lines. Variable rate of change varies at different points, creating curved graphs like parabolas or exponential functions.

What formula calculates constant rate of change?

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The formula is: Rate of Change = (y₂ - y₁)/(x₂ - x₁). This gives you the slope between any two points. For constant rate, this value stays the same regardless of which points you choose.

More Constant Rate of Change Questions

Click on any question to see the complete solution with step-by-step explanations

Variation of a Function

Find the Rate of Change: Solving -x+y=0 Linear Equation Find the Rate of Change in the Linear Equation: -5x+y=3 Find the Rate of Change in the Linear Equation 3-y=1/4x Find the Rate of Change in Linear Equation -8y+2x=6 Find the Rate of Change: Solving -1/4y + x = 3

Continue Your Math Journey

Master Constant Rate of Change first, then advance to these related topics that build on your fraction skills

Suggested Topics to Practice in Advance

Ways to Represent a FunctionRepresenting a Function Verbally and with TablesGraphical Representation of a FunctionAlgebraic Representation of a FunctionNotation of a Function

Topics Learned in Later Sections

Rate of Change of a FunctionVariation of a FunctionRate of change represented with steps in the graph of the functionRate of change of a function represented graphicallyVariable Rate of ChangeRate of Change of a Function Represented by a Table of ValuesFunctions for Seventh GradeIncreasing and Decreasing Intervals (Functions)Increasing functionsDecreasing functionConstant FunctionDecreasing Interval of a functionIncreasing Intervals of a functionDomain of a FunctionIndefinite integralInputing Values into a Function

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