Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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

How do you determine the initial fee in a linear function context?

Back

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

Front

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

Back

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

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 slopes of two linear functions?

Back

You can compare the coefficients of x in their equations. The function with the larger coefficient has a greater slope.

Front

What does it mean if a linear function has a negative slope?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

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).

Front

What is the difference between a greater slope and a lesser slope in terms of steepness?

Back

A greater slope means the line is steeper, indicating a faster rate of change, while a lesser slope indicates a gentler incline.

Front

How do you identify the greater rate of change between two linear equations?

Back

Compare the slopes of the equations; the one with the larger slope value has the greater rate of change.