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 of a line represent?

Back

The slope of a line 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 of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0.

Front

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

Back

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

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a function has a positive slope, what does that indicate about the function?

Back

A positive slope indicates that as x increases, y also increases.

Front

If a function has a negative slope, what does that indicate about the function?

Back

A negative slope indicates that as x increases, y decreases.

Front

What does it mean if two functions have the same slope?

Back

If two functions have the same slope, they have the same rate of change, but they may have different y-intercepts.

Front

How can you determine which of two linear functions has a greater rate of change?

Back

You can compare their slopes; the function with the larger slope has a greater rate of change.