To determine the equation of the line shown in the graph, we can follow these steps:

1. Find the slope (m):

   • The slope of a line is calculated as the change in $y$ (rise) divided by the change in $x$ (run) between two points on the line.
   • From the graph, we can observe two points that lie on the line. One appears to be $(-6, 3)$, and the other appears to be $(0, -2)$, which is also the y-intercept.

   Using the formula for slope $m$:

   $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 3}{0 - (-6)} = \frac{-5}{6}$

   So, the slope is $m = -\frac{5}{6}$.

2. Identify the y-intercept (b):

   • From the graph, the line crosses the $y$-axis at $(0, -2)$, so the y-intercept $b = -2$.

3. Write the equation:

   • The equation of a line in slope-intercept form is $y = mx + b$. Substituting the values of $m$ and $b$:

   $y = -\frac{5}{6}x - 2$

Thus, the equation of the line is $y = -\frac{5}{6}x - 2$.

Would you like a detailed explanation of any part of this process?

Here are some related questions:

1. How do you calculate the slope if the points aren't given explicitly?
2. What is the point-slope form of a line?
3. How do you convert point-slope form to slope-intercept form?
4. How do you graph a line if you are only given the equation?
5. Can you find the equation of a line if you are given only the slope and a point?

Tip: Always double-check the coordinates you pick from the graph to ensure the calculation is accurate!