The problem is to determine the equation of the line shown in the graph.

1. Problem Description

The problem is to determine the equation of the line shown in the graph.

2. Solution Steps

First, we identify two points on the line from the graph. It looks like the line passes through $(0, 2)$ and $(4, -4)$.

We can calculate the slope $m$ of the line using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Using the two points $(0, 2)$ and $(4, -4)$, we have $x_1 = 0$, $y_1 = 2$, $x_2 = 4$, and $y_2 = -4$.

Therefore,

$m = \frac{-4 - 2}{4 - 0} = \frac{-6}{4} = -\frac{3}{2}$.

The equation of the line can be written in slope-intercept form as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

We already found the slope $m = -\frac{3}{2}$. From the graph, we can see that the line intersects the y-axis at $y=2$, so the y-intercept $b = 2$.

Therefore, the equation of the line is $y = -\frac{3}{2}x + 2$.

3. Final Answer

$y = -\frac{3}{2}x + 2$