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).