Real World Problems Writing Linear Functions

Front

What is a linear function?

Back

A linear function is a mathematical function that creates a straight line when graphed. 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 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 or fixed cost in real-world problems.

Front

In the equation y = mx + b, what does 'm' represent?

Back

In the equation, 'm' represents the slope of the line, which indicates the rate of change of y with respect to x.

Front

What is the slope in a real-world context?

Back

The slope represents the rate at which one quantity changes in relation to another, such as cost per item or monthly fees.

Front

How do you identify the fixed cost in a real-world problem involving linear functions?

Back

The fixed cost is represented by the y-intercept in the equation, which is the cost incurred regardless of the quantity consumed.

Front

What is the equation for calculating total cost with a fixed fee and a variable fee?

Back

The total cost can be calculated using the equation: Total Cost = Fixed Fee + (Variable Fee per unit * Number of units).

Front

If a gym charges a one-time registration fee and a monthly fee, how would you model the total cost after 'x' months?

Back

Total Cost = Registration Fee + (Monthly Fee * x).

Front

What does it mean if a cost is variable?

Back

A variable cost changes based on the level of activity or usage, such as the number of games played or data used.

Front

How can you determine the total amount saved over time with a monthly saving plan?

Back

Total Amount Saved = Initial Amount + (Monthly Savings * Number of Months).

Front

What is the difference between fixed costs and variable costs?

Back

Fixed costs remain constant regardless of the level of activity, while variable costs change with the level of activity.