Linear Functions

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

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 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 equation of a line in slope-intercept form?

Back

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

Front

What is the dependent variable in a linear function?

Back

The dependent variable is the variable that depends on the value of the independent variable, typically represented as y in the equation y = mx + b.

Front

What is the independent variable in a linear function?

Back

The independent variable is the variable that is manipulated or changed, typically represented as x in the equation y = mx + b.

Front

How can you determine if a relationship is linear from a table of values?

Back

A relationship is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the independent variable (x) increases, the dependent variable (y) decreases.