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To find the equation relating \( x \) and \( y \) for the points on this line, we can use the given points on the line to determine the slope and then form the linear equation.

### Step-by-Step Solution

1. **Identify Points on the Line**:
   We have two specific points on the line:
   - \( (2, -4) \)
   - \( (10, 3) \)  (point \( C \))

2. **Calculate the Slope**:
   The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Using the points \( (2, -4) \) and \( (10, 3) \):
   \[
   m = \frac{3 - (-4)}{10 - 2} = \frac{3 + 4}{8} = \frac{7}{8}
   \]

3. **Form the Equation**:
   We can use the point-slope form of a line:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using the point \( (2, -4) \) and the slope \( \frac{7}{8} \):
   \[
   y - (-4) = \frac{7}{8}(x - 2)
   \]
   Simplify this to get:
   \[
   y + 4 = \frac{7}{8}x - \frac{7}{4}
   \]
   Subtract 4 from both sides to isolate \( y \):
   \[
   y = \frac{7}{8}x - \frac{7}{4} - 4
   \]
   Converting \( 4 \) to a fraction with denominator 4:
   \[
   y = \frac{7}{8}x - \frac{7}{4} - \frac{16}{4}
   \]
   \[
   y = \frac{7}{8}x - \frac{23}{4}
   \]

### Final Equation
The equation of the line relating \( x \) and \( y \) is:
\[
y = \frac{7}{8}x - \frac{23}{4}
\]

Would you like a detailed explanation on any part of this solution or have further questions?

### Related Questions
1. How can you convert the slope-intercept form to the standard form of a line?
2. What are some ways to check if a point lies on a line given its equation?
3. How do you interpret the slope in real-world scenarios?
4. What other forms of line equations exist besides slope-intercept and point-slope?
5. Can you find an equation of a line perpendicular to this one?

### Tip:
Always double-check your calculations, especially when converting between fraction forms, as small errors can lead to incorrect equations.

The points (2, -4), (x, y), A, and B all lie on the line. Find an equation relating x and y.

Learn how to find the equation of a line passing through given points using slope calculation and linear equations. This problem covers key concepts like slope formula and point-slope form, suitable for students in Grades 8-10.

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