A linear model for each situation passes through the origin....

A linear model for each situation passes through the origin. Find each missing value. Round your answer to the nearest tenth.
.8 .5 gal of gas to drive $243.1 \mathrm{mi}, 3$ gal of gas to drive mi.

Key Concepts

Rounding

Rounding is the process of simplifying a number to a required degree of precision, typically to make it easier to read or to meet specific instructions. In this problem, answers are rounded to the nearest tenth to provide a practical level of detail.

Linear Models Passing Through the Origin

A linear model that passes through the origin is defined by the equation y = mx, where y and x are variables and m is the constant rate of change. Because the line goes through the origin, when x equals zero, y is also zero, illustrating a direct proportional relationship between the variables.

Slope

The slope in a linear equation represents the constant rate of change between the dependent and independent variables. It is calculated as the change in the dependent variable divided by the change in the independent variable and, in this context, gives the amount of distance traveled per unit of gas used.

Proportional Reasoning

Proportional reasoning involves working with quantities that have a constant ratio. When a model goes through the origin, it implies that the relationship between the variables is proportional, allowing one to use multiplication to scale the known ratio to find missing values.

Unit Rate

The unit rate is the measure of one quantity per one unit of another quantity, such as miles per gallon in a driving scenario. It is derived from the slope and is crucial for predicting unknown values via direct multiplication.

Transcript

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