F4 (Constructing Function to Model Linear Relationship)

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 line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you calculate the total cost for a service with a fixed fee and a variable fee?

Back

Total cost = Fixed fee + (Variable fee per unit * Number of units). For example, if a service has a $50 fixed fee and charges $40 per month, the total cost for t months is c = 50 + 40t.

Front

What is the formula for calculating the cost of joining a gym with a joining fee and monthly dues?

Back

Cost = Joining fee + (Monthly dues * Number of months). For example, if the joining fee is $50 and monthly dues are $40, the cost for t months is c = 50 + 40t.

Front

What does a rate of change indicate in a linear relationship?

Back

The rate of change indicates how much the dependent variable (y) changes for each unit increase in the independent variable (x). In a linear function, this is constant.

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the initial value in a linear function?

Back

The initial value is the value of the dependent variable (y) when the independent variable (x) is zero. It corresponds to the y-intercept of the function.

Front

How do you interpret the equation c = 40t + 50?

Back

In this equation, c represents the total cost, t represents the number of months, 40 is the monthly fee, and 50 is the one-time joining fee.

Front

What is a real-world example of a linear function?

Back

An example of a linear function is the cost of a taxi ride, where there is a base fare plus a charge per mile driven.