Concept 2

Interpret parameters (slope, intercept, coefficients) in terms of the context.

Read each parameter with its unit and with its role in the expression.

Core Idea

In a model, each parameter has a job. Read it with its unit and with its position in the expression.

Understanding

Rule: Read each parameter with its unit.

The coefficient tells how the output changes for a 1-unit change in the input.
The constant term is the starting amount when the input is 0.
Rewrite each number in words before you choose the interpretation.

Step by Step

Identify what the input variable measures and what the output represents.
Locate the coefficient of the variable and the constant term.
Attach units to each number and translate each one back into the context.

Misconceptions

Treating the intercept as the rate because it appears first in the equation.
Dropping the units and giving a numerical answer that does not describe a real quantity.
Assuming every coefficient is a starting value instead of asking how the variable changes the output.

Question

Worked Example

A taxi fare is modeled by $𝐹 = 3.25 + 2.10 𝑚$ , where $𝐹$ is the fare in dollars and $𝑚$ is the number of miles traveled. Which interpretation is correct?

Select an answer to see the explanation