To solve this, I'll extract key information from the graph and determine the equation of the line in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Let me analyze the graph. PIL import Image import pytesseract

Load the uploaded image

image_path = "/mnt/data/173464603304491uoxxqr.jpg" image = Image.open(image_path)

Use OCR to extract text for analysis (if needed for interpreting numbers)

extracted_text = pytesseract.image_to_string(image) extracted_textThe graph shows a line plotted over the range $[-5, 5]$ for both x- and y-axes. I will manually determine the slope and y-intercept based on the line’s appearance.

The steps are as follows:

1. Identify two clear points on the line.
2. Calculate the slope $m = \frac{y_2 - y_1}{x_2 - x_1}$.
3. Use the slope-intercept form, $y = mx + b$, to find the equation.

Let me zoom into the graph to identify points for precise calculations. Enhance the image to focus on the graph for manual analysis import matplotlib.pyplot as plt

Display the uploaded image for manual interpretation of points

plt.imshow(image) plt.axis('on') # Turn on the axis for reference plt.title("Uploaded Graph for Analysis") plt.show()From the graph, two clear points on the line can be identified as approximately:

• $(-5, 0)$
• $(0, -5)$

Step 1: Calculate the slope ($m$):

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the points: $m = \frac{-5 - 0}{0 - (-5)} = \frac{-5}{5} = -1$

Step 2: Find the y-intercept ($b$):

The y-intercept is the value of $y$ when $x = 0$. From the graph, $b = -5$.

Step 3: Write the equation:

The equation of the line is: $y = -x - 5$

Let me know if you'd like a detailed explanation or have questions about this process!

Here are 5 related questions to expand your understanding:

1. What is the slope of a vertical line?
2. How do you find the x-intercept of a line given its equation?
3. What happens to the equation of a line if the slope becomes positive?
4. Can a line have a slope of 0? If so, what does its equation look like?
5. How can you rewrite $y = -x - 5$ in standard form?

Tip: When identifying points from a graph, choose points where the line crosses grid intersections for maximum precision.