Classify Graphs and Equations as Linear or Nonlinear

The video tutorial covers the identification of linear and nonlinear functions through equations and graphs. It begins with an introduction to the learning objectives, followed by a detailed explanation of linear functions, including their characteristics and representation in slope-intercept form. The tutorial then explains nonlinear functions, highlighting their distinct features. The video includes practice sessions for identifying functions from graphs and classifying equations as linear or nonlinear, reinforcing the concepts taught.

What is a key characteristic of a linear function?

• It has a variable with an exponent greater than one.

• Its graph is a non-vertical straight line.

• It always forms a vertical line.

• It cannot be expressed in the form y = mx + b.

How can you identify a linear function from its equation?

• The equation has a variable with an exponent of two.

• The equation is in the form y = mx + b.

• The equation includes a division by a variable.

• The equation has a variable as an exponent.

Which of the following is NOT true about nonlinear functions?

• They can be expressed in the form y = mx + b.

• Their graphs are not straight lines.

• They have variables with exponents other than one.

• They do not have a constant rate of change.

Which graph represents a nonlinear function?

• A graph with a straight line.

• A graph with a curve.

• A graph with a vertical line.

• A graph with a horizontal line.

What is the slope of the line in the equation y = 2/3x - 5?

• 0

• -5

• 2/3

• 1

Which equation represents a nonlinear function?

• y = x

• y = 3/x

• y = x/5

• y = 2x + 1

In the equation y = x^3, why is it considered nonlinear?

• It forms a straight line.

• It is in the form y = mx + b.

• The exponent of x is 1.

• The exponent of x is 3.