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

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 represented as (0, b) in the equation y = mx + b.

Front

How do you find the slope from 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 independent variable in a linear function?

Back

The independent variable is the variable that represents the input of the function, often denoted as x.

Front

What is the dependent variable in a linear function?

Back

The dependent variable is the variable that represents the output of the function, often denoted as y.

Front

What does the equation y = -x + 2 represent?

Back

This equation represents a linear function with a slope of -1 and a y-intercept of 2.

Front

How do you identify the y-intercept from the equation y = 5x - 4?

Back

The y-intercept is found by setting x = 0. In this case, y = -4, so the y-intercept is (0, -4).

Front

What is the slope of the line represented by the equation y = 1/2x + 7?

Back

The slope of the line is 1/2.

Front

What is the significance of the slope being negative?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases, resulting in a downward slant of the line.