We are given a linear function $f(x) = \frac{2}{3}x - 4$. We need to identify the slope, the vertical intercept (y-intercept), and the horizontal intercept (x-intercept). Finally, we need to draw the graph of the function.

1. Problem Description

We are given a linear function $f(x) = \frac{2}{3}x - 4$. We need to identify the slope, the vertical intercept (y-intercept), and the horizontal intercept (x-intercept). Finally, we need to draw the graph of the function.

2. Solution Steps

The given linear function is in the slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

In our case, $f(x) = \frac{2}{3}x - 4$, so the slope $m = \frac{2}{3}$ and the y-intercept $b = -4$. The y-intercept is the point $(0, -4)$.

To find the x-intercept, we set $f(x) = 0$ and solve for $x$:

$0 = \frac{2}{3}x - 4$

$\frac{2}{3}x = 4$

$x = 4 \cdot \frac{3}{2}$

$x = 6$

So, the x-intercept is $(6, 0)$.

The slope is $\frac{2}{3}$. The y-intercept is -4, and the x-intercept is

6.

3. Final Answer

Slope: $\frac{2}{3}$

Vertical Intercept: -4

Horizontal Intercept: 6