Identifying Linear Functions and Characteristics

The video tutorial explains how to identify equations with a constant rate of change, focusing on linear functions. It covers the characteristics of linear functions in graphs, equations, and tables, emphasizing the importance of a constant rate of change. Common mistakes in identifying linearity are discussed, and examples of linear and non-linear equations are analyzed. The lesson concludes with a summary of the key points covered.

What is the main difference between the equations y = 5 + 2x and y = 5 + 2x^2?

• y = 5 + 2x^2 has a constant rate of change, while y = 5 + 2x does not.

• Both are non-linear functions.

• y = 5 + 2x has a constant rate of change, while y = 5 + 2x^2 does not.

• Both have a constant rate of change.

How can you identify a linear function from its graph?

• It forms a curved line.

• It has multiple intercepts.

• It forms a straight line.

• It has varying slopes.

In a table, what indicates a linear function?

• The change in y is always positive.

• The change in x is always negative.

• The ratio of change in y to change in x is constant.

• The values of y are all the same.

What is a common mistake when identifying linear functions in tables?

• Ignoring the change in x.

• Using only the first and last values.

• Only considering the change in y.

• Calculating the average of y values.

What does a negative coefficient in a linear equation indicate?

• The y-values increase as x increases.

• The y-values decrease as x increases.

• The function has no intercept.

• The function is non-linear.

How does the equation y = 5 + 2x indicate a linear function?

• The coefficient of x is zero.

• The coefficient of x is constant.

• The equation has an exponent.

• The equation has no constant term.

Why is y = 5 + 2x^2 not a linear function?

• It forms a straight line on a graph.

• It has no y-intercept.

• It includes an exponent on x.

• It has a constant rate of change.

What happens to the graph of a function if it is not linear?

• It forms a straight line.

• It has multiple y-intercepts.

• It forms a curved line.

• It has no slope.

What role does the exponent play in determining if a function is linear?

• Exponents do not affect linearity.

• An exponent of 0 indicates non-linearity.

• An exponent greater than 1 indicates non-linearity.

• An exponent of 1 indicates non-linearity.

Which of the following is a characteristic of a linear function?

• The table values are random.

• The equation includes an exponent.

• The rate of change is constant.

• The graph is a parabola.