Comparing Functions

Front

What is the definition of slope in the context of a linear function?

Back

The slope of a linear function is the rate of change of the function, representing how much the output (y) changes for a unit change in the input (x). It is often denoted as 'm' in the equation y = mx + b.

Front

How do you determine which of two linear functions has a greater rate of change?

Back

To determine which of two linear functions has a greater rate of change, compare their slopes. The function with the larger slope value has the greater rate of change.

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 between the two variables.

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 between the two variables.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the linear function crosses the y-axis, representing the value of the output (y) when the input (x) is zero.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified from a graph by its straight line appearance, indicating a constant rate of change (slope) between the variables.

Front

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

Back

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

Front

What is the difference between a linear function and a nonlinear function?

Back

A linear function has a constant rate of change and can be represented by a straight line, while a nonlinear function has a variable rate of change and cannot be represented by a straight line.

Front

What is the rate of change for a function represented by the equation y = 3x + 2?

Back

The rate of change (slope) for the function y = 3x + 2 is 3.

Front

How do you find the initial value of a linear function from its equation?

Back

The initial value of a linear function can be found by identifying the y-intercept, which is the constant term in the equation (b in y = mx + b).