Linear Equations Word 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 variable 'y' represent in a linear equation?

Back

In a linear equation, 'y' typically represents the dependent variable, which is the output or result of the equation based on the value of 'x'.

Front

What is the slope in a linear equation?

Back

The slope (m) in a linear equation represents the rate of change of 'y' with respect to 'x'. It indicates how steep the line is.

Front

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

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of 'y' when 'x' is 0.

Front

How do you write an equation for a word problem involving a fixed cost and a variable cost?

Back

You write the equation by adding the fixed cost to the product of the variable cost per unit and the number of units. For example, C = fixed cost + (variable cost per unit * x).

Front

What is the equation for Juanita's monthly cell phone bill if she uses x minutes of airtime?

Back

C = 15 + 0.20x, where C is the total bill.

Front

How can you identify the dependent and independent variables in a word problem?

Back

The independent variable is usually the one you can control or change (like 'x' minutes), while the dependent variable is what you measure or calculate (like 'y' cost).

Front

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

Back

It represents a situation where there are 120 gallons of water in a tank, and it releases water at a rate of 25 gallons per minute.

Front

How do you determine the total cost of a taxi ride based on distance traveled?

Back

You can determine the total cost by using the equation y = mx + b, where m is the cost per mile, x is the number of miles, and b is the flat fee.

Front

What is the equation for the total cost of a camp for a family with x additional children?

Back

y = 225x + 625, where y is the total cost and x is the number of additional children.