Real World Problems Writing Linear Functions

What is a linear function?

• A function that creates a curve when graphed.

• A mathematical function that creates a straight line when graphed.

• A function that has no slope.

• A function that can only be expressed in the form of a quadratic equation.

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

• The value of y when x is 0, representing the starting point or fixed cost in real-world problems.

• The slope of the line, indicating the rate of change of y with respect to x.

• The point where the line crosses the x-axis, indicating the value of x when y is 0.

• The maximum value of y that the function can achieve.

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

• Total Cost = Fixed Fee + (Variable Fee per unit * Number of units)

• Total Cost = Fixed Fee - (Variable Fee per unit * Number of units)

• Total Cost = (Fixed Fee * Number of units) + Variable Fee

• Total Cost = Fixed Fee / (Variable Fee per unit * Number of units)

What is the difference between fixed costs and variable costs?

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

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

• Fixed costs are incurred only during production, while variable costs are incurred at all times.

• Fixed costs are always higher than variable costs.

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

• The y-intercept of the line

• The slope of the line, which indicates the rate of change of y with respect to x

• The x-intercept of the line

• The constant term in the equation

What does it mean if a cost is variable?

• A variable cost remains constant regardless of the level of activity.

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

• A variable cost is fixed and does not change over time.

• A variable cost is only applicable to fixed assets.

What is the slope in a real-world context?

• The slope is the angle of a line on a graph.

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

• The slope is always a positive number.

• The slope indicates the total distance covered.

What is an example of a real-world problem that can be modeled with a linear function?

• Calculating the total cost of a cell phone plan that has a monthly fee and a charge per gigabyte of data used.

• Determining the population growth of a species over time.

• Calculating the area of a circle based on its radius.

• Estimating the time it takes to travel a distance at a constant speed.

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

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

• Total Amount Saved = Initial Amount - (Monthly Savings * Number of Months)

• Total Amount Saved = (Monthly Savings * Number of Months) / Initial Amount

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

What is the significance of the constant term in a linear equation?

• It represents the slope of the line.

• It indicates the direction of the line.

• It represents the initial value or starting point in a real-world scenario, such as a fixed fee.

• It determines the steepness of the line.