Suppose you are a fitness instructor and want to determine...

Suppose you are a fitness instructor and want to determine the number of calories a client burns during a workout. From exercise tables, you find that during the first part of the workout (aerobics) she will burn 220 calories. During the optional second part of the workout (swimming), she will burn 7.8 calories per minute. a. Write a linear model in slope-intercept form that gives the total number of calories $c$ that the client burns if she concludes a workout with $m$ minutes of swimming. b. Many fitness instructors recommend that a client burn 300 calories per exercise session to lose weight. How many minutes of swimming should the client perform to satisfy this requirement?

Suppose you are a fitness instructor and want to determine the number of calories a client burns during a workout. From exercise tables, you find that during the first part of the workout (aerobics) she will burn 220 calories. During the optional second part of the workout (swimming), she will burn 7.8 calories per minute.
a. Write a linear model in slope-intercept form that gives the total number of calories $c$ that the client burns if she concludes a workout with $m$ minutes of swimming.
b. Many fitness instructors recommend that a client burn 300 calories per exercise session to lose weight. How many minutes of swimming should the client perform to satisfy this requirement?

Key Concepts

Solving Linear Equations

Solving linear equations involves isolating the variable to determine its value that satisfies the equation. This process is essential for finding an unknown quantity, such as the number of minutes of an activity needed to reach a target outcome.

Real-World Applications

Applying linear models to real-world scenarios, like fitness tracking, helps in making predictions and informed decisions based on calculated relationships. This includes planning activities to achieve specific goals, such as burning a set number of calories.

Interpretation of Parameters

Interpreting the parameters in a linear equation involves recognizing the real-world meaning of the slope and y-intercept. In a fitness context, the y-intercept might indicate the calories burned in a fixed part of the workout, while the slope represents calories burned per minute in an activity.

Slope-Intercept Form

The slope-intercept form of a linear equation, given as y = mx + b, provides a straightforward way to capture a linear relationship. Here, m represents the slope, which is the rate of change, and b is the y-intercept, which is the starting value or initial condition.

Linear Model

A linear model represents a relationship between two quantities using a straight line. In many contexts, such as fitness or finance, it is used to predict an outcome based on a fixed starting value and a constant rate of change.

Transcript

Please give Ace some feedback