Linear Functions Word Problems

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

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

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

Back

The y-intercept (b) 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 write an equation for a total cost based on fixed and variable costs?

Back

The equation can be written in the form y = mx + b, where m is the variable cost per unit, x is the number of units, and b is the fixed cost.

Front

If a DJ charges a setup fee and an hourly fee, how would you represent the total cost?

Back

The total cost can be represented as y = mx + b, where m is the hourly fee, x is the number of hours, and b is the setup fee.

Front

What is the equation for a situation where a plumber charges a flat fee plus an hourly rate?

Back

The equation would be y = mx + b, where m is the hourly rate, x is the number of hours worked, and b is the flat fee.

Front

How do you interpret the equation y = -25x + 120?

Back

This equation represents a situation where there are initially 120 units (e.g., gallons of water) and it decreases by 25 units for each unit of x (e.g., time in minutes).

Front

What does it mean if the slope of a linear function is negative?

Back

A negative slope indicates that as x increases, y decreases. This represents a decrease in the quantity being measured.

Front

How can you determine the total cost of an activity with a fixed fee and a variable fee?

Back

You can determine the total cost by adding the fixed fee to the product of the variable fee and the number of units (e.g., hours or items).

Front

What is the equation for Bob's savings if he saves a fixed amount each month?

Back

The equation is y = 40x + 150, where y is the total savings, x is the number of months, 40 is the amount saved per month, and 150 is the initial amount.