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 dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

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 is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

What does the point (3, 27) represent in a linear function context?

Back

The point (3, 27) represents $27 for 3 shirts, indicating a relationship between the number of shirts and their total cost.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified from a graph if it forms a straight line.

Front

What is the significance of the slope being positive or negative?

Back

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

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you graph a linear function?

Back

To graph a linear function, identify the y-intercept (b), plot it on the y-axis, and use the slope (m) to find another point.