Writing Equations from Context

Front

What is the general form of a linear equation used to represent a real-world situation?

Back

The general form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you set up an equation from a word problem involving a fixed cost and a variable cost?

Back

Identify the fixed cost and the variable cost per unit, then express the total cost as the sum of the fixed cost and the variable cost multiplied by the number of units.

Front

In the context of a word problem, what does 'x' typically represent?

Back

'x' usually represents the unknown quantity that you are trying to solve for.

Front

What is the first step in solving a word problem that requires writing an equation?

Back

Read the problem carefully to identify the quantities involved and the relationships between them.

Front

How can you determine the total cost in a problem involving multiple items with different prices?

Back

Multiply the price of each item by the number of items purchased and sum all the costs.

Front

What does the term 'total charge' refer to in a rental scenario?

Back

The total charge is the sum of the fixed rental fee and any additional costs based on usage, such as mileage.

Front

How do you isolate a variable in an equation?

Back

Use inverse operations to move all terms involving the variable to one side of the equation and constant terms to the other side.

Front

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

Back

The slope indicates the rate of change of the dependent variable with respect to the independent variable.

Front

How do you interpret the y-intercept in a real-world context?

Back

The y-intercept represents the value of the dependent variable when the independent variable is zero.

Front

What is a fixed cost in a business scenario?

Back

A fixed cost is a cost that does not change with the level of goods or services produced.