Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and 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, indicating how much y changes for a unit change in x.

Front

How do you determine the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (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, 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 graphs?

Back

If two linear functions have the same slope, their graphs are parallel and will never intersect.

Front

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

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

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

How can you tell which linear function has a greater slope by comparing their equations?

Back

The slope is the coefficient of x in the equation y = mx + b; the function with the larger coefficient has the greater slope.

Front

What is the significance of the y-intercept in real-world applications?

Back

The y-intercept can represent the starting value of a situation, such as initial cost or starting population.

Front

How do you compare the steepness of two linear functions?

Back

You compare the slopes; the function with the larger slope value is steeper.