Linear Functions Word Problems

Front

What is a linear function?

Back

A linear function is a 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 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 linear function from a word problem?

Back

Identify the variables, determine the rate of change (slope), and the starting value (y-intercept), then write the equation in the form y = mx + b.

Front

If a tank releases water at a rate of 25 gallons per minute, how would you express this as a linear equation?

Back

y = -25x + 120, where y is the amount of water left in the tank after x minutes.

Front

What is the equation for the total cost of renting a snowboard if the resort charges $15 per hour and $25 for the board?

Back

y = 15x + 25, where y is the total cost and x is the number of hours.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

Front

How do you determine the total cost from a rental fee and hourly charge?

Back

Add the fixed rental fee to the product of the hourly charge and the number of hours rented.

Front

What is the equation for the total charges for Easy Car Rental if they charge $8.50 an hour plus a rental fee of $25.50?

Back

y = 25.5 + 8.5x, where y is the total charge and x is the number of hours.

Front

What is the significance of the negative slope in the equation y = -25x + 120?

Back

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