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 linear function represent?

Back

The slope of a linear function represents the rate of change of y with respect to x. It indicates how much y increases or decreases for a unit increase in x.

Front

What is the y-intercept of a 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 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 are constant for equal intervals of x.

Front

What is the slope of the equation y = 2x + 5?

Back

The slope is 2.

Front

What is the y-intercept of the equation y = -4x + 1?

Back

The y-intercept is (0, 1).

Front

If a function has a slope of -3, what does this indicate about its graph?

Back

A slope of -3 indicates that for every 1 unit increase in x, y decreases by 3 units, resulting in a downward slant.

Front

What does it mean if a function is non-linear?

Back

A non-linear function does not graph to a straight line. Its rate of change varies, and it may curve or have different slopes at different points.

Front

Identify the slope of the equation y = 5 - 2x.

Back

The slope is -2.

Front

What is the general form of a linear equation?

Back

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