PIL import Image import pytesseract

Load the uploaded image to extract text

image_path = "/mnt/data/1733344923208bw03tvvw.jpg" extracted_text = pytesseract.image_to_string(Image.open(image_path))

extracted_textThe text extraction from the image seems incomplete or distorted. Let me manually interpret and transcribe the equations accurately from the image:

1. $y = -x + 3$
2. $y = -4x - 1$
3. $2x - y = 1$
4. $x + 2y = -8$
5. $8x + 3y = -9$
6. $4x + 5y = -10$
7. $x - y = -2$
8. $4x - 3y = 9$

Now, I'll identify the slope ($m$) and y-intercept ($b$) for each equation. Define a function to extract slope and y-intercept def get_slope_intercept(equation): # Reformat the equation to slope-intercept form y = mx + b if "y" in equation and "=" in equation: lhs, rhs = equation.split("=") lhs = lhs.strip() rhs = rhs.strip() if lhs == "y": # Directly in slope-intercept form terms = rhs.split() slope = float(terms[0].replace("x", "")) if "x" in terms[0] else 0 intercept = float(terms[1]) if len(terms) > 1 else 0 else: # Bring y to the LHS and format terms = lhs.split() for term in terms: if "y" in term: slope = float(rhs.split()[0].replace("x", "").strip()) # Here are the steps to calculate the slope ($m$) and $y$-intercept ($b$) for each equation:

1. $y = -x + 3$:

   • Slope (m): -1
   • Y-intercept (b): 3

2. $y = -4x - 1$:

   • Slope (m): -4
   • Y-intercept (b): -1

3. $2x - y = 1$ (Rewritten: $y = 2x - 1$):

   • Slope (m): 2
   • Y-intercept (b): -1

4. $x + 2y = -8$ (Rewritten: $y = -\frac{1}{2}x - 4$):

   • Slope (m): $-\frac{1}{2}$
   • Y-intercept (b): -4

5. $8x + 3y = -9$ (Rewritten: $y = -\frac{8}{3}x - 3$):

   • Slope (m): $-\frac{8}{3}$
   • Y-intercept (b): -3

6. $4x + 5y = -10$ (Rewritten: $y = -\frac{4}{5}x - 2$):

   • Slope (m): $-\frac{4}{5}$
   • Y-intercept (b): -2

7. $x - y = -2$ (Rewritten: $y = x + 2$):

   • Slope (m): 1
   • Y-intercept (b): 2

8. $4x - 3y = 9$ (Rewritten: $y = \frac{4}{3}x - 3$):

   • Slope (m): $\frac{4}{3}$
   • Y-intercept (b): -3

Let me know if you'd like further details or clarifications on these calculations.

Relative Questions

1. How do you rewrite equations into slope-intercept form?
2. What does the slope tell us about the line?
3. How can we graph a line using its slope and y-intercept?
4. What happens if the slope is zero or undefined?
5. How does the slope relate to parallel or perpendicular lines?

Tip

Always arrange your equation in the form $y = mx + b$ to easily identify the slope and y-intercept.