linear functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented 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 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 in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value).

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, and A should be non-negative.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, y also increases. This is indicated by a positive slope.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, y decreases. This is indicated by a negative slope.

Front

What is the difference between a function and a non-function?

Back

A function has one output for each input, while a non-function can have multiple outputs for a single input.

Front

How can you identify the slope from a linear equation in slope-intercept form?

Back

In the slope-intercept form y = mx + b, the slope is represented by m.

Front

Back

The slope of the line is -\frac{3}{2}.