The problem is to graph the function $f(x) = \frac{4}{5}x + 6$. This is a linear function in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. Problem Description

The problem is to graph the function $f(x) = \frac{4}{5}x + 6$. This is a linear function in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

2. Solution Steps

First, identify the slope and y-intercept.

The slope $m = \frac{4}{5}$.

The y-intercept $b = 6$. This means the line crosses the y-axis at the point $(0, 6)$.

Now, find another point on the line. We can use the slope to find another point. Starting from the y-intercept $(0, 6)$, we can go "rise over run". In this case the rise is 4 and the run is

5. Therefore, from $(0, 6)$, move 5 units to the right and 4 units up to find the next point on the line. This gives us the point $(0+5, 6+4) = (5, 10)$.

Alternatively, we could pick an x value, such as $x=5$, and plug it into the equation:

$f(5) = \frac{4}{5}(5) + 6 = 4 + 6 = 10$. Thus, the point $(5, 10)$ is on the line.

Graph the line by plotting the y-intercept $(0, 6)$ and the point $(5, 10)$ and drawing a straight line through them.

3. Final Answer

The graph of the function $f(x) = \frac{4}{5}x + 6$ is a straight line that passes through the points $(0, 6)$ and $(5, 10)$. I would plot these two points on a graph and draw a line connecting them.