Characteristics of 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 is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers, meaning it can take any value for x.

Front

How do you find the x-intercept of a linear function?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What is the significance of the x-intercept?

Back

The x-intercept is the point where the line crosses the x-axis, represented as (a, 0) in the equation.

Front

What is the standard form of a linear equation?

Back

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

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.