Let's analyze the image.

The task is to write the equation of the line in fully simplified slope-intercept form. The slope-intercept form of a line is:

$y = mx + b$

where:

• $m$ is the slope of the line.
• $b$ is the y-intercept (the value of $y$ when $x = 0$).

Step 1: Identify two points on the line

Looking at the graph:

• One point is $(-10, -8)$.
• Another point is $(0, -4)$.

Step 2: Calculate the slope $m$

The formula for 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 $(-10, -8)$ and $(0, -4)$: $m = \frac{-4 - (-8)}{0 - (-10)} = \frac{-4 + 8}{10} = \frac{4}{10} = \frac{2}{5}$

Step 3: Find the y-intercept $b$

From the graph, the y-intercept is $-4$ (since the line crosses the y-axis at $y = -4$).

Step 4: Write the equation

Now that we have the slope $m = \frac{2}{5}$ and the y-intercept $b = -4$, the equation of the line in slope-intercept form is:

$y = \frac{2}{5}x - 4$

This is the required equation.

Do you need further clarification or have any questions?

Here are 5 related questions:

1. How do you convert between slope-intercept form and standard form?
2. What does the slope represent in real-world applications?
3. How can you determine if two lines are parallel or perpendicular?
4. How do you find the x-intercept of a line from its equation?
5. What happens to the graph of a line if the slope increases?

Tip: When finding the slope between two points, always pay attention to the signs to avoid calculation errors.