linear functions

Front

What is 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 linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

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

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 x-intercept of the equation 4x - 10y = 20?

Back

The x-intercept is 5.

Front

What is the y-intercept of the equation 4x - 10y = 20?

Back

The y-intercept is -2.

Front

What does the y-intercept represent in a real-world context?

Back

The y-intercept represents the initial value of the dependent variable when the independent variable is zero.

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 determine if a function is linear from a table of values?

Back

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

Front

What is the graph of the equation y = -x + 2?

Back

The graph is a straight line that crosses the y-axis at (0, 2) and the x-axis at (2, 0).