Applying Linear Functions Review

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and 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 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 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 do you calculate the total cost of attending an event with a fixed admission fee and a variable cost per ride?

Back

Total Cost = Admission Fee + (Cost per Ride * Number of Rides). For example, if the admission fee is $5 and each ride costs $0.50, the total cost for 30 rides would be $5 + (0.50 * 30) = $20.

Front

Write the equation in slope-intercept form for a situation where a family pays a fixed fee plus an additional amount for each extra child.

Back

The equation is y = mx + b, where m is the additional cost per child and b is the fixed fee. For example, if the fixed fee is $625 and the additional cost is $225 per child, the equation is y = 225x + 625.

Front

If Jacob collects 2 hats a week and starts with 6 hats, how can this situation be modeled with a linear equation?

Back

The situation can be modeled by the equation y = 2x + 6, where y is the total number of hats after x weeks.

Front

What does it mean if a linear function has a positive slope?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does it mean if a linear function has a negative slope?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

How can you identify the slope from a graph of a linear function?

Back

The slope can be identified by selecting two points on the line and calculating the rise over run (change in y over change in x).

Front

What is the significance of the y-intercept in real-life situations?

Back

The y-intercept often represents a starting value or initial condition in real-life situations, such as initial costs or starting quantities.