Comparing 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 f(x) = 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 the output (y) changes for a unit change in the input (x).

Front

How do you find the rate of change from a graph?

Back

To find the rate of change from a graph, select two points on the line, (x1, y1) and (x2, y2), and use the formula: Rate of Change = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of 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 can you compare the rates of change of two linear functions?

Back

You can compare the rates of change by looking at their slopes. The function with the greater slope has a greater rate of change.

Front

What is the formula for calculating the slope between two points?

Back

The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is: m = (y2 - y1) / (x2 - x1).

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.

Front

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 do you determine the initial fee from a linear cost function?

Back

The initial fee is represented by the y-intercept (b) in the linear equation of the cost function.

Front

What is the significance of the slope in a real-world context?

Back

In a real-world context, the slope can represent rates such as speed, cost per item, or any other rate of change.