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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.EE.B.5

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).

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.HSF-LE.A.1B

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.

Tags

CCSS.HSF.LE.B.5

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.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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).

Tags

CCSS.HSF.LE.B.5