Systems: 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 it mean to break even?

Back

Breaking even means that total revenues equal total costs, resulting in neither profit nor loss.

Front

How do you represent a cost function for a service with a fixed fee and a variable cost?

Back

The cost function can be represented as C(x) = fixed fee + (variable cost per unit * x), where x is the number of units.

Front

What is the slope in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you set up an equation to compare costs from two different companies?

Back

Set the cost equations of both companies equal to each other to find the number of units where costs are the same.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions to the system are the values that satisfy all equations simultaneously.

Front

How do you find the number of items needed to break even?

Back

To find the break-even point, set the total revenue equal to total costs and solve for the number of items (x).

Front

What is a variable in an equation?

Back

A variable is a symbol (often x or y) that represents an unknown value in an equation.

Front

What does it mean to solve a word problem?

Back

Solving a word problem involves translating the written scenario into mathematical equations and then finding the solution.