Linear or Nonlinear Equations, tables, and graphs

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear equation?

Back

A nonlinear equation is an equation that does not form a straight line when graphed. Examples include quadratic equations like y = x² or exponential equations like y = 2^x.

Front

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

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

Back

A function is linear if the change in y-values is constant for equal changes in x-values.

Front

What is the graph of a linear equation?

Back

The graph of a linear equation is a straight line that can extend infinitely in both directions.

Front

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

Back

A linear function has a constant rate of change and graphs as a straight line, while a nonlinear function has a variable rate of change and graphs as a curve.

Front

Can a linear equation have a negative slope?

Back

Yes, a linear equation can have a negative slope, which means the line goes down as you move from left to right.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x², which graphs as a parabola.

Front

What does it mean for an equation to be in slope-intercept form?

Back

An equation is in slope-intercept form if it is written as y = mx + b, where m is the slope and b is the y-intercept.