The function you provided is $f(x) = \frac{2}{3}x + 1$. This is a linear function of the form $f(x) = mx + b$, where:

• $m = \frac{2}{3}$ is the slope of the line.
• $b = 1$ is the y-intercept of the line, which is the point where the line crosses the y-axis.

Key Features of the Function:

1. Slope: The slope $\frac{2}{3}$ indicates that for every increase of 1 unit in $x$, the value of $f(x)$ increases by $\frac{2}{3}$. This represents a gradual upward incline.

2. Y-Intercept: The line crosses the y-axis at the point (0, 1).

3. Graph: The graph is a straight line with a positive slope, slanting upwards from left to right.

4. Domain and Range:

   • Domain: All real numbers ($x \in \mathbb{R}$).
   • Range: All real numbers ($f(x) \in \mathbb{R}$).

5. Behavior: The function is increasing since the slope is positive.

Would you like a detailed explanation of any aspect, or perhaps a graph?

Related Questions:

1. What is the x-intercept of the function $f(x) = \frac{2}{3}x + 1$?
2. How does changing the slope affect the graph of a linear function?
3. How would the function change if the y-intercept was different?
4. Can you determine the rate of change between any two points on this line?
5. What is the significance of the slope in real-world applications?

Tip: Always remember, the slope tells you how steep a line is, and the y-intercept shows where the line crosses the y-axis!