Linear or Non-Linear?

How can you tell if a function is linear by looking at its equation?

• If it can be written in the form y = mx + b, where m and b are constants.

• If it has a constant rate of change that is not zero.

• If it contains variables raised to powers greater than one.

• If it intersects the y-axis at the origin.

What does it mean if a function is represented by a straight line on a graph?

• It indicates that the function is quadratic, meaning it has a variable rate of change.

• It indicates that the function is linear, meaning it has a constant rate of change.

• It indicates that the function is exponential, meaning it grows rapidly.

• It indicates that the function is logarithmic, meaning it decreases over time.

What is an example of a nonlinear function?

• y = 2x + 3

• y = x^2

• y = 5

• y = 1/x

What is the difference between a linear equation and a nonlinear equation?

• A linear equation can be written in the form y = mx + b, while a nonlinear equation may include variables raised to powers other than one, such as y = x^2 or y = sin(x).

• A linear equation has a constant slope, while a nonlinear equation has a variable slope.

• A linear equation can only have one variable, while a nonlinear equation can have multiple variables.

• A linear equation is always a straight line, while a nonlinear equation can never be a straight line.

What is a linear function?

• A function that can be graphically represented as a straight line and has a constant rate of change.

• A function that curves and does not have a constant rate of change.

• A function that can only be represented in a quadratic form.

• A function that has no relationship between variables.

What is a table of values?

• A method to organize data in rows and columns for easy access.

• A way to organize pairs of x and y values to analyze the relationship between them, often used to determine if a function is linear or nonlinear.

• A chart that displays only the x values of a function.

• A graphical representation of data points on a coordinate plane.

What is the y-intercept in a linear function?

• The point where the graph crosses the x-axis.

• The value of y when x is 0.

• The slope of the line.

• The maximum value of y in the function.

Can a linear function have a negative slope?

• Yes, a linear function can have a negative slope, which means that as x increases, y decreases.

• No, a linear function cannot have a negative slope.

• A linear function can only have a positive slope.

• A linear function can have a slope of zero.

What is a constant rate of change?

• A constant rate of change means that for every unit increase in x, the change in y is always the same, characteristic of linear functions.

• A constant rate of change indicates that y changes at a variable rate depending on x.

• A constant rate of change refers to the slope of a quadratic function.

• A constant rate of change is when y does not change regardless of x.

How can you determine if a function is linear from a table of values?

• Check if the differences between consecutive y-values are constant when the x-values increase by the same amount.

• Look for a pattern in the x-values only.

• Ensure that all y-values are positive.

• Verify that the x-values are in ascending order.