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.

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.

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.

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.

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.

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.

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.

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.

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.