Ready to challenge your math skills? Take our free linear and nonlinear relations quiz and put your knowledge to the test! You'll learn to quickly spot linear vs nonlinear relations, practice solving linear tables, identify linear relations quiz-style, master key linear relations formulas, and even try a mini nonlinear relations practice test. Tailored for students, teachers, and lifelong learners, this quiz boosts your confidence before important exams - think beyond a simple practice session and gear up for your linear relationships unit test . When you want more, explore our linear functions quiz to solidify every concept. Ready to dive in and shine? Start now and celebrate every aha moment!
What is the common difference in the sequence 5, 8, 11, 14, ...?
2
3
4
5
An arithmetic sequence has a constant difference between consecutive terms. Here 8 ? 5 = 3, and 11 ? 8 = 3, so the pattern holds. Thus the common difference is 3. For more on arithmetic sequences, see Mathsisfun - Sequences.
Which equation represents a linear function?
y = 3x + 2
y = x^2 + 1
y = 1/x
y = 2^x
Linear functions are of the form y = mx + b, where m and b are constants. Only y = 3x + 2 matches that form. The others include variable exponents or reciprocals. Read more at Mathsisfun - Linear Equations.
Determine if the relation {(1, 2), (2, 4), (3, 6), (4, 8)} is linear.
Only if extended
No
Yes
Cannot determine
The points satisfy y = 2x, which is a linear function with slope 2. The change in y over change in x is constant at 2. Thus the relation is linear. See Khan Academy - Linear Equations for more.
What is the slope of the line passing through the points (2, 3) and (5, 11)?
4
3/8
2
8/3
Slope is calculated as (11 ? 3)/(5 ? 2) = 8/3. This ratio of vertical change to horizontal change defines a constant rate. More examples at Mathsisfun - Slope.
Which of the following is a nonlinear relation?
y = 2x + 5
y = ?x + 1
y = 4x
y = x^2 + 3x + 2
Nonlinear relations include variables raised to powers other than one. y = x^2 + 3x + 2 is quadratic, so it is nonlinear. The others are straight lines. See Mathsisfun - Nonlinear Functions.
What is the y-intercept of the line y = ?4x + 7?
7
1
?4
0
The y-intercept occurs when x = 0, so y = ?4·0 + 7 = 7. That gives the point (0, 7). Learn more at Mathsisfun - Slope-Intercept.
Which of these is the slope-intercept form of a linear equation?
y = b + mx^2
y = mx + b
x = by + m
Ax + By = C
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. The other forms are standard linear, mixed, or nonlinear. More at Khan Academy - Linear Equations.
Given the function y = 4x + 3, what is the value of y when x = ?2?
?5
?11
11
5
Substitute x = ?2: y = 4(?2) + 3 = ?8 + 3 = ?5. This shows direct evaluation of a linear function. See Mathsisfun - Functions.
Find the explicit formula for the arithmetic sequence 2, 5, 8, 11, ... .
a_n = 5n + 2
a_n = 2n + 3
a_n = 3n ? 1
a_n = 4n ? 2
The common difference is 3 and the first term is 2. Substituting n = 1 into a_n = 3n ? 1 gives 2, matching the sequence. Hence, a_n = 3n ? 1. More at Khan Academy - Sequences.
Which of the following equations represents a quadratic relation?
y = 1/x
y = 2^x
y = 5x + 2
y = x^2 ? 4x + 3
Quadratic relations have a squared term and highest exponent 2. Only y = x^2 ? 4x + 3 fits that definition. Others are linear, exponential, or inverse. Read more at Mathsisfun - Quadratics.
Does the table below represent a linear relation? x: 1, 2, 3, 4; y: 2, 4, 8, 16
Only for x > 4
No
Yes
Cannot determine
A linear relation has constant differences in y. Here y doubles each time (2 ? 4 ? 8 ? 16) so the differences are not constant. This is exponential behavior. See Khan Academy - Types of Functions.
Identify the type of relation given by y = 3 * 2^x.
Constant
Quadratic
Exponential
Linear
Exponential relations involve a constant base raised to the variable exponent. Here base 2 is raised to x, making it exponential. More at Mathsisfun - Exponential Functions.
Which equation represents an inverse variation between x and y?
y = 5x + 2
y = 5/x
y = x^5
y = 5x
Inverse variation has the form y = k/x. Only y = 5/x matches that pattern; others are direct variation or linear with additive terms. See Khan Academy - Inverse Proportion.
Which of the following represents a direct variation?
y = 4x + 1
y = x^2
y = 4x
y = 4/x
Direct variation is y = kx without an added constant. Here k = 4 in y = 4x. The others include constants or reciprocal terms. More at Mathsisfun - Direct Variation.
What is the average rate of change of y = ?2x + 4 between x = 1 and x = 3?
2
?1
?2
1
For a linear function, the average rate of change equals the constant slope m. Here m = ?2, so the rate of change over any interval is ?2. See Khan Academy - Slope.
For the function y = x^2, what is the rate of change from x = 2 to x = 3?
4
3
5
7
Rate of change = (f(3) ? f(2))/(3 ? 2) = (9 ? 4)/1 = 5. Quadratic functions have nonconstant rates of change. More at Mathsisfun - Quadratics.
What is the general form of a quadratic function?
y = ax^2 + bx + c
y = ax^3 + bx^2 + c
y = a^x
y = mx + b
Quadratic functions are second-degree polynomials of the form ax^2 + bx + c. The degree is defined by the highest exponent, which is 2. Other forms represent linear, exponential, or cubic relations. See Khan Academy - Quadratic Equations.
Find the x-intercept of the line given by 2x + 3y = 12.
4
?6
6
0
The x-intercept occurs when y = 0. Substituting gives 2x = 12, so x = 6. The intercept is (6, 0). More at Mathsisfun - Intercepts.
Find the vertex of the parabola defined by y = x^2 ? 6x + 8.
(3, ?1)
(?3, ?1)
(3, 1)
(1, ?6)
The vertex h = ?b/(2a) = 6/2 = 3. Substituting x = 3 gives y = 9 ? 18 + 8 = ?1. Thus, vertex = (3, ?1). See Khan Academy - Vertex Form.
Which equation represents a line perpendicular to y = 3x ? 5 and passing through the point (0, 2)?
y = ?1/3x + 2
y = 1/3x + 2
y = 3x + 2
y = ?3x + 2
Perpendicular slopes are negative reciprocals. The slope of the given line is 3, so the perpendicular slope is ?1/3. Through (0, 2) the equation is y = ?1/3x + 2. More at Mathsisfun - Perpendicular Lines.
Is the equation xy + 2y = 5 linear or nonlinear?
Neither
Both
Nonlinear
Linear
The term xy multiplies variables together, making it nonlinear. Linear equations have variables only to the first power and not multiplied by each other. For more, see Wikipedia - Linear Equation.
Which of the following graphs represents a hyperbola?
y = ?x + 1
y = x^2
y = 2^x
y = 1/x
A hyperbola arises from inverse relations such as y = 1/x, producing two separate branches. Quadratic produces a parabola, exponential grows rapidly, and linear is a straight line. Read about conic sections at Mathsisfun - Conic Sections.
Which of the following is the vertex form of a quadratic function?
y = ax^2 + bx + c
y = a^x + k
y = a(x ? h)^2 + k
y = mx + b
Vertex form isolates the vertex at (h, k) in y = a(x ? h)^2 + k. Standard form ax^2 + bx + c does not directly show the vertex. See Mathsisfun - Quadratic Equations.
Classify the function y = 2x^3 + x as which type of relation?
Cubic
Quadratic
Linear
Exponential
This polynomial has the highest exponent 3, so it is a cubic function. Linear has degree 1, quadratic has degree 2, and exponential has variable in the exponent. More at Khan Academy - Polynomial Functions.
Classify the relation defined implicitly by the equation x^2 + y^2 = 1; is it linear or nonlinear?
Only if y is constant
Cannot be determined
Nonlinear
Linear
The equation includes squared terms of x and y, making it nonlinear. Linear relations only involve first-degree terms. x^2 + y^2 = 1 defines a circle, not a straight line. See Wikipedia - Linear Equation.
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Study Outcomes
Understand Core Concepts -
Grasp the foundational characteristics of linear and nonlinear equations as a basis for the linear and nonlinear relations quiz.
Distinguish Relation Types -
Learn to spot the key differences between linear vs nonlinear relations by analyzing patterns in tables, equations, and graphs.
Identify Linear Formulas -
Practice extracting linear relations formulas from datasets, reinforcing the skills tested in the identify linear relations quiz.
Solve Values in Linear Tables -
Apply systematic techniques to complete and interpret linear tables, predicting missing values with confidence.
Analyze Graphical Patterns -
Interpret graphs to classify relations, recognize slopes and intercepts, and distinguish straight lines from curves.
Apply Principles in Practice -
Put your skills to the test with nonlinear relations practice test scenarios, preparing you for advanced algebra challenges.
Cheat Sheet
Slope and Rate of Change -
Understanding that slope (m) represents the constant rate of change in linear equations is key. It's calculated as Δy/Δx, or "rise over run," a mnemonic highlighted by Khan Academy and many university algebra guides. Practicing this formula helps build confidence in identifying linear relations on tables and graphs.
Y-Intercept and Equation Forms -
Recognize that linear relations can be written in slope-intercept form, y = mx + b, where b indicates the y-intercept. The National Council of Teachers of Mathematics emphasizes mastering both point-slope and slope-intercept formats to flexibly model real-world scenarios. This knowledge streamlines solving and graphing tasks on your identify linear relations quiz.
Constant vs. Variable Change -
Review table patterns by checking if differences in y-values are constant as x increments by equal steps; constant differences signal linear relations. When those differences vary, you're dealing with nonlinear relations, like quadratic or exponential patterns. Purdue University's resources stress table analysis for quick classification before graphing.
Recognizing Common Nonlinear Types -
Familiarize yourself with prototypical nonlinear relations - quadratic (y = ax² + bx + c), exponential (y = a·bˣ), and others - each showing a changing rate of change. Using sample data from official college algebra texts helps you spot curves and accelerations instead of straight lines. A handy trick: if the second differences in a table are constant, you're likely looking at a quadratic relation.
Graph Interpretation Strategies -
Boost your graphing skills by sketching or analyzing plotted points to confirm straight or curved patterns; this approach is a staple in preparing for any linear and nonlinear relations quiz. The American Mathematical Society recommends cross-checking by calculating slopes between multiple point pairs to verify constancy. With this strategy, you'll confidently tackle both linear vs nonlinear relations challenges.
