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 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

How do you find the rate of change from a linear equation?

Back

The rate of change can be found from the equation y = mx + b, where m is the coefficient of x. This coefficient represents the slope.

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 represented by the value of b in the equation y = mx + b.

Front

If two linear functions have the same slope, what can be said about their rates of change?

Back

If two linear functions have the same slope, they have the same rate of change.

Front

How can you compare the rates of change of two linear functions given their equations?

Back

You can compare the rates of change by looking at the slopes (m values) of the equations. The function with the greater slope has a greater rate of change.

Front

What is the significance of the slope in real-world applications?

Back

In real-world applications, the slope can represent speed, cost per item, or any other rate of change, helping to compare different scenarios.

Front

How do you determine which linear function is cheaper based on their equations?

Back

To determine which function is cheaper, calculate the output (y value) for the same input (x value) and compare the results.

Front

What does it mean if two linear functions intersect?

Back

If two linear functions intersect, it means they have the same output (y value) for a specific input (x value), indicating a point of equality.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).