Linear Functions Word Problems

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.

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

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.

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.

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.

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.

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).

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

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).

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.