Let’s analyze the graph and determine the slope-intercept form of the equation for the line. Here's how we solve this step by step:

Step 1: Recall the 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 (where the line crosses the y-axis).

Step 2: Determine the slope $m$

The slope is calculated using two points on the line: $m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

From the graph:

• Point 1: $(-6, 6)$
• Point 2: $(0, -2)$

Using these points: $m = \frac{-2 - 6}{0 - (-6)} = \frac{-8}{6} = -\frac{4}{3}$

So, the slope is $m = -\frac{4}{3}$.

Step 3: Find the y-intercept $b$

The y-intercept ($b$) is the point where the line crosses the y-axis. From the graph, this occurs at $(0, -2)$. Thus, $b = -2$.

Step 4: Write the equation

Now that we know $m = -\frac{4}{3}$ and $b = -2$, the equation of the line is: $y = -\frac{4}{3}x - 2$

Final Answer:

The equation of the line in slope-intercept form is: $y = -\frac{4}{3}x - 2$

Would you like further details or assistance? Here are some related questions:

1. How do we verify the slope using different points on the line?
2. What is the significance of slope in real-world contexts?
3. Can you explain how to convert this equation to standard form?
4. How do we graph a line starting from the slope-intercept form equation?
5. What is the impact of changing the slope or intercept values?

Tip: Always choose clear points on the graph (where the line crosses grid intersections) to calculate the slope accurately.