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

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

Back

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

Front

What does the slope of a line represent?

Back

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

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

If a line has a slope of 0, what does that indicate?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.

Front

What is the slope of the line that passes through the points (2, 5) and (6, 1)?

Back

The slope is m = (1 - 5) / (6 - 2) = -4 / 4 = -1.

Front

How can you identify the slope from the equation y = 2x + 4?

Back

The slope is the coefficient of x, which is 2.

Front

What is the rate of change in a linear function?

Back

The rate of change is the same as the slope; it measures how much y changes for a unit change in x.

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope indicates a vertical line, where x remains constant while y changes.