Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept (b) in the equation y = mx + b?

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 do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

What does a zero slope indicate about a linear function?

Back

A zero slope indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate about a linear function?

Back

An undefined slope indicates that the line is vertical, meaning x does not change as y changes.

Front

How do you write the equation of a line in slope-intercept form?

Back

To write the equation in slope-intercept form, identify the slope (m) and the y-intercept (b) and use the format y = mx + b.

Front

What is the difference between a function and not a function?

Back

A function has only one output (y) for each input (x), while a relation that is not a function has at least one input (x) with multiple outputs (y).