Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope in a linear function?

Back

The slope (m) of a linear function represents the rate of change of y with respect to x. It indicates how steep the line is.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How can you determine if a relationship is linear from a graph?

Back

A relationship is linear if the graph forms a straight line. If the graph curves or has bends, it is nonlinear.

Front

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

Back

A linear function has a constant rate of change and can be represented by a straight line, while a nonlinear function does not have a constant rate of change and can be represented by curves or other shapes.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

If a graph passes through the points (1, 2) and (3, 6), is it linear?

Back

Yes, because the points form a straight line.

Front

What does it mean if a function is described as 'nonlinear'?

Back

A nonlinear function does not form a straight line when graphed and may involve curves, quadratics, exponentials, etc.

Front

How can you identify a linear equation from a table of values?

Back

If the differences between consecutive y-values are constant for equal differences in x-values, the equation is linear.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.