Understand Linear Functions Flashcard

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 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 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 table of values represents a linear function?

Back

A table represents a linear function if the differences between consecutive y-values are constant when the x-values increase by the same amount.

Front

What is the general form of a linear equation?

Back

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

Front

Is the equation y + 4 = 2x linear or nonlinear?

Back

Linear. It can be rearranged to the form y = 2x - 4.

Front

Can a linear function have a vertical line as its graph?

Back

False. A linear function cannot have a vertical line as its graph; it must be a straight line that is not vertical.

Front

What does it mean if a function is nonlinear?

Back

A nonlinear function does not create a straight line when graphed. Its rate of change varies.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients determine the slope and the y-intercept of the line, affecting its steepness and position.

Front

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

Back

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