Constructing Functions (8.F.4)

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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

How do you identify the slope in a linear function?

Back

The slope in a linear function is the coefficient of x in the equation y = mx + b. It represents the rate of change of y with respect to x.

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the function on the y-axis.

Tags

CCSS.HSF.LE.B.5

Front

How can you model a real-world situation using a linear function?

Back

To model a real-world situation, identify the quantities involved, determine how they change in relation to each other, and express this relationship in the form of a linear equation.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

In the context of a pizza purchase, how would you express the cost as a function of the number of toppings?

Back

The cost can be expressed as y = 0.50x + 8, where y is the total cost, x is the number of toppings, and 8 is the base cost of the pizza.

Tags

CCSS.HSF-BF.A.1A

Front

What is the significance of the service fee in a plumbing charge model?

Back

The service fee is a fixed cost that is added to the variable cost (hourly rate) in the model, represented as y = 15x + 40.

Tags

CCSS.HSF.LE.B.5

Front

How do you interpret the equation y = 10x + 115 in the context of a speeding ticket?

Back

In this equation, y represents the total cost of the ticket, x represents the number of miles per hour over the speed limit, 10 is the cost per mile over, and 115 is the fixed court cost.

Tags

CCSS.HSF.LE.B.5

Front

What does the equation y = 65x represent in terms of travel?

Back

This equation represents the total distance traveled (y) as a function of time (x) at a constant speed of 65 miles per hour.

Tags

CCSS.HSF.LE.B.5

Front

How does depreciation affect the value of an asset over time?

Back

Depreciation reduces the value of an asset by a fixed amount each year, as shown in the equation y = -200x + 1500, where y is the value after x years.