Comparing Linear Functions

Front

What is the rate of change (slope) in a linear function?

Back

The rate of change (slope) in a linear function represents how much the output (y) changes for a unit change in the input (x). It is calculated as the change in y divided by the change in x.

Front

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

Back

The y-intercept of a linear function is the value of y when x is 0. It represents the starting point of the function on the y-axis.

Front

How do you determine which linear function is cheaper for a given input?

Back

To determine which linear function is cheaper, compare the outputs (costs) of each function for the same input value (e.g., number of movies). The function with the lower output is cheaper.

Front

What is the equation of a linear function?

Back

A linear function can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the input (x) increases, the output (y) also increases, showing a direct relationship.

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What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the input (x) increases, the output (y) decreases, showing an inverse relationship.

Front

How can you find the slope from a graph of a linear function?

Back

To find the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then divide rise by run.

Front

What is the significance of the one-time fee in a linear cost function?

Back

The one-time fee is represented by the y-intercept in a linear cost function, indicating the initial cost before any variable charges are applied.

Front

How do you compare the rates of change of two linear functions?

Back

To compare the rates of change, look at the slopes of the functions. The function with the greater slope has a higher rate of change.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, characterized by a constant rate of change and can be represented by a linear equation.