To write the equation of the line shown in the graph, we need two key elements: the slope of the line and the y-intercept.

Step 1: Identify two points on the line

From the graph, the line passes through the following points:

1. $(-5, -8)$
2. $(0, -3)$
3. $(5, 2)$

Step 2: Calculate the slope (m)

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Using the points $(-5, -8)$ and $(0, -3)$: $m = \frac{-3 - (-8)}{0 - (-5)} = \frac{-3 + 8}{5} = \frac{5}{5} = 1$

So, the slope $m = 1$.

Step 3: Identify the y-intercept (b)

The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at the point $(0, -3)$. Therefore, the y-intercept $b = -3$.

Step 4: Write the equation of the line

The equation of a line in slope-intercept form is:

$y = mx + b$

Substituting $m = 1$ and $b = -3$, we get:

$y = x - 3$

Final Answer:

The equation of the line is:

$y = x - 3$

Would you like more details on how this was solved, or do you have any questions?

Follow-up Questions:

1. How do we calculate the slope if given different points?
2. What is the point-slope form of a line's equation?
3. Can we determine the slope if a line is vertical or horizontal?
4. How can we convert a slope-intercept equation to standard form?
5. What happens to the equation if we shift the line vertically by 3 units?

Tip:

Remember, the slope represents the "rise over run," or how much the line goes up or down for each unit it moves horizontally.