Understanding Linear and Nonlinear Equations

The video tutorial provides an overview of linear and nonlinear equations, explaining that linear equations can be graphed as straight lines and are expressed in the form y = mx + b. Nonlinear equations, on the other hand, cannot be graphed as straight lines and may include exponents, roots, or multiple variables. Examples of linear equations with fractions and decimals are given, and reasons for nonlinearity are discussed, such as the presence of exponents or multiple variables. The tutorial concludes with an invitation for questions.

What is a key characteristic of a linear equation?

• It cannot be graphed.

• It can be graphed as a line.

• It always includes an exponent.

• It must have three variables.

Which of the following is an example of a linear equation?

• y = 2x + 5y + 4z = 10

• y = √x + 3

• y = x^2 + 2

• y = 2x + 1

What type of graph is a parabola?

• Nonlinear

• Elliptical

• Linear

• Circular

Which form is used to identify a linear equation?

• y = mx + b

• y = ax^2 + bx + c

• y = x^2 + b

• y = √x + b

Which of the following is NOT a characteristic of a nonlinear equation?

• Graphing as a straight line

• Presence of roots

• Presence of exponents

• Involvement of multiple variables

What happens to a linear equation when it includes an exponent?

• It remains linear.

• It becomes nonlinear.

• It becomes a quadratic equation.

• It becomes undefined.

Which of the following equations is nonlinear?

• y = 2x + 1

• y = x^2 + 2

• y = 0.213x + 4.7

• y = 13x - 13

What is a common feature of nonlinear equations?

• They can be graphed as straight lines.

• They often include exponents or roots.

• They are always quadratic.

• They always have two variables.

Which of the following is a reason an equation might be nonlinear?

• It has no variables.

• It is a constant equation.

• It includes a square root.

• It is in the form y = mx + b.

What is required to graph an equation with three variables?

• A circular graph

• A three-dimensional space

• A two-dimensional plane

• A single line