What is the slope of the linear function and its units?  Select an answer miles dollars per mile miles per dollar dollars Correct - select the correct units

What is the 𝑦-intercept and its units? Correct Select an answer miles dollars Correct - select the correct units

What is the linear function, 𝐶(𝑥)? 𝐶(𝑥)=   

Question HelpQuestion 17: 

*Forum* Post to forum

Let's break down the problem step by step, based on the given context:

1. **Slope of the Linear Function and Its Units:**

   We already found that the slope (\( m \)) of the linear function is \(-\frac{8}{9}\). The slope represents the rate of change of the function, which is the change in \( y \) divided by the change in \( x \).

   To determine the units, we look at the units associated with \( y \) and \( x \). Since \( y \) represents the output (e.g., dollars) and \( x \) represents the input (e.g., miles), the slope's units will be the units of \( y \) per unit of \( x \).

   - If \( y \) is dollars and \( x \) is miles, the slope's units are dollars per mile.

   Therefore, the slope is \(-\frac{8}{9}\) dollars per mile.

2. **\( y \)-Intercept and Its Units:**

   The \( y \)-intercept (\( b \)) is \(-\frac{5}{9}\). The \( y \)-intercept represents the value of the function when \( x = 0 \).

   The units of the \( y \)-intercept are the same as the units of \( y \), which in this case would be dollars.

   Therefore, the \( y \)-intercept is \(-\frac{5}{9}\) dollars.

3. **Linear Function \( C(x) \):**

   Given that \( x \) represents miles and \( y \) represents dollars, the linear function \( C(x) \) can be written as:

   \[
   C(x) = -\frac{8}{9}x - \frac{5}{9}
   \]

In summary:

- The slope of the linear function is \(-\frac{8}{9}\) dollars per mile.
- The \( y \)-intercept is \(-\frac{5}{9}\) dollars.
- The linear function \( C(x) \) is:

  \[
  C(x) = -\frac{8}{9}x - \frac{5}{9}
  \]

Would you like any further details or have any questions about this solution?

Here are 5 questions you might ask next:
1. How do I interpret the slope and \( y \)-intercept in a real-world context?
2. Can you explain how to convert fractions to decimals and vice versa?
3. How do changes in the slope and \( y \)-intercept affect the graph of a linear function?
4. What are some real-life examples of linear functions with their slopes and intercepts?
5. Can you show me how to find the equation of a line given a point and the slope?

**Tip:** Always consider the context of the problem to determine the appropriate units for the slope and intercept, ensuring your interpretation aligns with real-world meanings.

Explore the concepts of linear functions, including slope and y-intercept calculation. Learn how to determine the slope of a linear function in dollars per mile, understand the meaning of y-intercept in dollars, and calculate the function C(x) = -8/9x - 5/9 step-by-step.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation