Understanding Linear Functions and Slope

The video tutorial explains how to determine if a graph represents a linear or non-linear function. It highlights that a linear function is characterized by a straight line and a constant rate of change, also known as slope. In contrast, a non-linear function is identified by curves and a lack of constant rate of change. The tutorial provides examples to illustrate these concepts, emphasizing the importance of understanding the rate of change in analyzing functions.

What is the first step in determining if a graph represents a linear or non-linear function?

• Check if the graph is colored.

• See if the graph is labeled.

• Count the number of points on the graph.

• Determine if the graph curves or is straight.

What characteristic of a graph indicates it is non-linear?

• It is horizontal.

• It is a straight line.

• It has a constant slope.

• It curves.

What does a straight line on a graph signify?

• The function is quadratic.

• The function is undefined.

• The function has a constant rate of change.

• The function is non-linear.

What is another term for the rate of change in a linear function?

• Axis

• Slope

• Intercept

• Vertex

How do you calculate the slope of a linear function?

• Divide the change in X by the change in Y.

• Multiply the change in Y by the change in X.

• Subtract the change in Y from the change in X.

• Divide the change in Y by the change in X.

In a linear function, what does a constant rate of change imply?

• The graph is a parabola.

• The graph is a circle.

• The graph is a straight line.

• The graph is curved.

What is the slope of a function if the change in Y is 5 and the change in X is 1?

• 5

• 10

• 1

• 0.2

What indicates a non-linear function in terms of rate of change?

• A constant rate of change.

• A positive rate of change.

• A variable rate of change.

• A negative rate of change.

If a function's rate of change is not constant, what type of function is it?

• Linear

• Non-linear

• Quadratic

• Exponential

What is the change in Y if the values go from 5 to 7?

• 1

• 4

• 2

• 3