Alg Lessons 6.1-6.4 LINEAR FUNCTIONS

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 of a line represent?

Back

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate. It indicates how steep the line is and the direction it goes (positive or negative).

Front

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

Back

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 by the value of b in the equation y = mx + b.

Front

How can you identify the y-intercept from the equation y = 3x + 5?

Back

The y-intercept is 5, which means the line crosses the y-axis at the point (0, 5).

Front

What is the significance of the x-intercept in a linear function?

Back

The x-intercept is the point where the line crosses the x-axis. It can be found by setting y = 0 in the equation of the line.

Front

How do you find the x-intercept of the equation y = 2x - 6?

Back

Set y = 0: 0 = 2x - 6. Solving gives x = 3, so the x-intercept is (3, 0).

Front

What does it mean if a line has a slope of 0?

Back

A slope of 0 means the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Front

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

Back

An undefined slope means the line is vertical, indicating that there is no change in the x-value as the y-value changes.

Front

How do you determine the domain of a linear function?

Back

The domain of a linear function is all real numbers unless there are restrictions based on the context of the problem.