Given the linear function \( f(x) = -3x + 2 \), here are some key points and properties of this function:

1. **Slope**: The coefficient of \( x \) is the slope of the line. Here, the slope \( m = -3 \). This means the line decreases by 3 units vertically for every 1 unit it moves horizontally.

2. **Y-intercept**: The constant term is the y-intercept. Here, the y-intercept is 2. This means the line crosses the y-axis at the point \( (0, 2) \).

3. **X-intercept**: To find the x-intercept, set \( f(x) = 0 \) and solve for \( x \):
   \[
   0 = -3x + 2
   \]
   \[
   3x = 2
   \]
   \[
   x = \frac{2}{3}
   \]
   The x-intercept is \( \left( \frac{2}{3}, 0 \right) \).

4. **Graph**: This is a straight line with a negative slope, indicating it will tilt downwards from left to right. It crosses the y-axis at 2 and the x-axis at \( \frac{2}{3} \).

5. **Domain and Range**: 
   - **Domain**: The domain of this linear function is all real numbers, \( (-\infty, \infty) \).
   - **Range**: The range is also all real numbers, \( (-\infty, \infty) \).

Would you like a detailed explanation of any specific part?

Here are some related questions you might consider:
1. How do you find the slope of a line from an equation?
2. How do you graph a linear function?
3. What does the slope of a line represent?
4. How do you determine the x-intercept and y-intercept of a function?
5. What is the significance of the domain and range in a function?

**Tip**: When working with linear functions, the slope can tell you a lot about the behavior of the line (e.g., increasing or decreasing).

Understand how to solve and graph the linear function f(x) = -3x + 2. This lesson covers key algebraic concepts such as slope, intercepts, and graphing techniques. Suitable for students in Grades 6-8, this problem provides a detailed breakdown of finding intercepts and plotting the function on a graph.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation