To determine whether the given graph represents the linear equation $-2x - 5y = 10$, we need to check if the equation corresponds to the line plotted.

Step 1: Convert the equation to slope-intercept form.

The equation is given as: $-2x - 5y = 10$

Solve for $y$: $-5y = 2x - 10$ $y = -\frac{2}{5}x + 2$

Thus, the slope of the line is $-\frac{2}{5}$, and the y-intercept is $2$.

Step 2: Analyze the graph.

1. The y-intercept ($y$-value where $x = 0$) should be $2$. Check whether the graph passes through the point $(0, 2)$.
2. The slope indicates that for every increase of $5$ units in $x$, $y$ decreases by $2$. This translates to points such as $(0, 2)$, $(5, 0)$, and so on.

Step 3: Verify the points.

From the graph:

• Check if the line passes through $(0, 2)$.
• Check if the line passes through another point consistent with the slope (e.g., $(5, 0)$).

Let me verify these calculations visually on the graph and confirm the alignment with the equation.from PIL import Image import matplotlib.pyplot as plt

Load and display the uploaded image

image_path = "/mnt/data/17322018828505bhtbsnx.jpg" img = Image.open(image_path)

Display the image for further analysis

plt.figure(figsize=(8, 6)) plt.imshow(img) plt.axis('on') # Show axis for reference plt.title("Uploaded Graph - Verifying Line") plt.show()Matplotlib is building the font cache; this may take a moment.

<<ImageDisplayed>>successFrom the visual inspection of the graph:

1. The line appears to pass through the y-intercept at $(0, 2)$, which is consistent with the equation $y = -\frac{2}{5}x + 2$.
2. The slope of the line seems to match $-\frac{2}{5}$, as for every 5 units increase in $x$, $y$ decreases by 2 units (e.g., the points $(0, 2)$ and $(5, 0)$).

Conclusion:

The graph does represent the linear equation $-2x - 5y = 10$. The correct answer is True.

Would you like a deeper explanation or to discuss related concepts?

Here are 5 related questions to explore:

1. What is the importance of converting equations to slope-intercept form for graphing?
2. How do you determine the slope of a line from two points?
3. Can we verify the equation using the point-slope formula?
4. What happens if a point does not satisfy the equation of the line?
5. How would the graph change if the slope or intercept was altered?

Tip: Always verify a line by testing multiple points to ensure it satisfies the equation.