Equations Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that represents 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

How do you represent a total cost in a word problem involving a flat fee and a variable cost?

Back

The total cost can be represented by an equation that combines the flat fee and the variable cost, typically in the form C = variable_cost * quantity + flat_fee.

Front

What does the variable 'x' typically represent in application-based word problems?

Back

In application-based word problems, 'x' often represents the quantity of items, people, or time involved in the scenario.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is zero. It represents the starting point or initial value in a real-world context.

Front

How can you determine the number of items needed based on a total and a per-item cost?

Back

You can determine the number of items by rearranging the equation to solve for the quantity, typically using the formula: quantity = (total_cost - fixed_cost) / cost_per_item.

Front

What is the formula to calculate the number of cabins needed if you know the total number of people and the capacity of each cabin?

Back

The formula is: number_of_cabins = total_people / capacity_per_cabin, rounding up to the nearest whole number if necessary.

Front

How do you write an equation for a situation where a quantity increases by a constant amount over time?

Back

The equation can be written in the form y = mx + b, where m is the constant increase per time unit, and b is the initial quantity.

Front

What is the role of constants in linear equations?

Back

Constants in linear equations represent fixed values that do not change, such as initial costs or starting quantities.

Front

How do you interpret the slope of a linear equation in a real-world context?

Back

The slope represents the rate of change; in a cost problem, it indicates how much the total cost increases for each additional unit.

Front

What is the first step in solving a word problem involving equations?

Back

The first step is to identify the variables and what they represent in the context of the problem.