https://file.aiquickdraw.com/mathbot/file/1736953283872iycnp4ws.jpg

 PIL import Image
import pytesseract

# Load the uploaded image
image_path = "/mnt/data/1736953283872iycnp4ws.jpg"
image = Image.open(image_path)

# Extract text from the image
extracted_text = pytesseract.image_to_string(image)
extracted_textThe question is to find the equation of the line passing through the following points:

1. \( (3, 2) \) and \( (5, 7) \)
2. \( (-1, 6) \) and \( (5, -3) \)
3. \( (5, -2) \) and \( (-7, 4) \)

I will solve each case step by step.

---

### **1. Line through \( (3, 2) \) and \( (5, 7) \):**

1. **Find the slope (\(m\)):**
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{5 - 3} = \frac{5}{2}
   \]

2. **Use the point-slope form:**
   The equation is \( y - y_1 = m(x - x_1) \).

   Substituting \( m = \frac{5}{2} \) and \( (x_1, y_1) = (3, 2) \):
   \[
   y - 2 = \frac{5}{2}(x - 3)
   \]

3. **Simplify to slope-intercept form (\(y = mx + b\)):**
   \[
   y - 2 = \frac{5}{2}x - \frac{15}{2}
   \]
   \[
   y = \frac{5}{2}x - \frac{15}{2} + 2
   \]
   \[
   y = \frac{5}{2}x - \frac{11}{2}
   \]

**Final equation:** 
\[
y = \frac{5}{2}x - \frac{11}{2}
\]

---

### **2. Line through \( (-1, 6) \) and \( (5, -3) \):**

1. **Find the slope (\(m\)):**
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 6}{5 - (-1)} = \frac{-9}{6} = -\frac{3}{2}
   \]

2. **Use the point-slope form:**
   Substituting \( m = -\frac{3}{2} \) and \( (x_1, y_1) = (-1, 6) \):
   \[
   y - 6 = -\frac{3}{2}(x - (-1))
   \]
   \[
   y - 6 = -\frac{3}{2}(x + 1)
   \]

3. **Simplify to slope-intercept form:**
   \[
   y - 6 = -\frac{3}{2}x - \frac{3}{2}
   \]
   \[
   y = -\frac{3}{2}x - \frac{3}{2} + 6
   \]
   \[
   y = -\frac{3}{2}x + \frac{9}{2}
   \]

**Final equation:** 
\[
y = -\frac{3}{2}x + \frac{9}{2}
\]

---

### **3. Line through \( (5, -2) \) and \( (-7, 4) \):**

1. **Find the slope (\(m\)):**
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - (-2)}{-7 - 5} = \frac{6}{-12} = -\frac{1}{2}
   \]

2. **Use the point-slope form:**
   Substituting \( m = -\frac{1}{2} \) and \( (x_1, y_1) = (5, -2) \):
   \[
   y - (-2) = -\frac{1}{2}(x - 5)
   \]
   \[
   y + 2 = -\frac{1}{2}(x - 5)
   \]

3. **Simplify to slope-intercept form:**
   \[
   y + 2 = -\

Find the equation of the line passing through: a. (3, 2) and (5, 7); b. (-1, 6) and (5, -3); c. (5, -2) and (-7, 4).

Learn how to find the equation of a line passing through points like (3, 2) and (5, 7), (-1, 6) and (5, -3), and (5, -2) and (-7, 4). This solution explains slope calculation, point-slope, and slope-intercept forms in detail. Suitable for Grades 9-10.

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