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 of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

How do you find 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. It is represented by the value of b in the equation y = mx + b.

Front

What is the rate of change in a real-world context?

Back

The rate of change refers to how one quantity changes in relation to another. For example, in a cost function, it represents the cost per unit.

Front

If a function has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in x, the value of y increases by 2 units.

Front

How can you determine which linear function has the greatest initial fee?

Back

To determine which function has the greatest initial fee, compare the y-intercepts of the functions represented in the equations or tables.

Front

What is the formula for calculating the cost of renting a raft if the rate is $2.25 per hour?

Back

The cost (C) can be calculated using the formula C = 2.25 * h, where h is the number of hours rented.

Front

What does it mean if two linear functions are parallel?

Back

Two linear functions are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What is the difference between a fixed cost and a variable cost in a linear function?

Back

A fixed cost is a constant amount that does not change with the level of output (initial fee), while a variable cost changes with the level of output (cost per guest).