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Explain how to determine the slope in a word problem that uses a linear function.

1. **Identify the Variables**: Determine which quantities in the problem are changing and represent them as variables, typically \(x\) and \(y\).

2. **Understand the Context**: Read the problem carefully to understand the relationship between the variables. The slope represents the rate of change of one variable with respect to the other.

3. **Look for Key Phrases**: Phrases like "per", "for each", or "every" often indicate the slope. For example, "miles per hour" or "cost per item" suggests a rate of change.

4. **Set Up a Ratio**: If specific values are given, set up a ratio of the change in \(y\) (dependent variable) to the change in \(x\) (independent variable).

5. **Calculate the Slope**: Use the formula \([tex]\frac{{\Delta y}}{{\Delta x}}[/tex]\) to calculate the slope, where \(\Delta y\) is the change in \(y\) and \(\Delta x\) is the change in \(x\).

6. **Interpret the Slope**: Ensure your understanding of the slope makes sense within the context of the problem. The slope should reflect the rate at which one quantity changes in relation to the other.

Answer :

Final answer:

To determine the slope in a word problem that uses a linear function, identify the variables, determine the change in the dependent variable for a given change in the independent variable, and divide the changes to calculate the slope.

Explanation:

How to Determine the Slope in a Word Problem That Uses a Linear Function

The slope of a linear function can be determined by examining the relationship between the dependent and independent variables. In a word problem, the slope represents how the dependent variable changes for every one unit increase in the independent variable. To determine the slope, you need to identify the change in the dependent variable for a given change in the independent variable.

  1. Identify the independent and dependent variables in the word problem.
  2. Determine the change in the dependent variable for a given change in the independent variable.
  3. Divide the change in the dependent variable by the change in the independent variable to calculate the slope.

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