Linear Application Problems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope in a linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the line on the y-axis.

Front

How do you write an equation for a situation with a starting value and a constant rate of change?

Back

The equation can be written as y = mx + b, where m is the constant rate of change and b is the starting value.

Front

In the equation y = 15x + 80, what does 80 represent?

Back

In this equation, 80 represents the initial number of members in the fitness club before any monthly increases.

Front

If a rental fee is a fixed cost plus a variable cost per hour, how is the total cost represented?

Back

The total cost can be represented as y = fixed fee + (variable cost per hour * number of hours).

Front

What does the equation y = -25x + 120 represent in a real-world context?

Back

This equation represents a situation where there are initially 120 gallons of water in a tank, and water is being released at a rate of 25 gallons per minute.

Front

How do you determine the total cost of renting a boat if there is a deposit and a per-hour charge?

Back

The total cost can be calculated using the equation C = deposit + (per-hour charge * number of hours).

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients indicate the rate of change and the initial value in a linear relationship. They help define the slope and y-intercept.

Front

How can you identify a linear relationship from a word problem?

Back

Look for phrases indicating a constant rate of change, such as 'per hour', 'each month', or 'for every unit'. These suggest a linear relationship.