Deliveries The equation 25+0.25 p=c gives the cost c in...

Deliveries The equation $25+0.25 p=c$ gives the cost $c$ in dollars that a store charges to deliver an appliance that weighs $p$ pounds. Use the equation and a table to find the weight of an appliance that costs dollar 55 to deliver.

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Key Concepts

Linear Equations

A linear equation represents a relationship between two variables where the change in one variable is proportional to the change in the other. It is typically written in the form y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept (starting value when x is zero). This concept is fundamental in modeling scenarios that involve a constant rate of increase or decrease.

Solving Equations

Solving an equation involves isolating the variable to determine its value that satisfies the equality. This process typically includes operations such as addition, subtraction, multiplication, and division. In applied contexts, such as calculating a weight for a given delivery cost, it provides a systematic way to determine unknown values.

Slope and Intercept in Real-world Applications

In contexts like cost calculations, the slope represents how much the cost increases per unit of weight, while the intercept represents a fixed fee that does not change with the weight. Understanding these components helps to translate real-world conditions into mathematical models and interpret their meaning accurately.

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