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The problem asks for an equation of a line that is parallel to the given line \( y = \frac{3}{2}x + 4 \) and passes through the point \( (-4, 10) \).

### Step-by-Step Solution:

1. **Identify the slope**: 
   The slope of the given line \( y = \frac{3}{2}x + 4 \) is \( m = \frac{3}{2} \). Since parallel lines have the same slope, the slope of the new line will also be \( \frac{3}{2} \).

2. **Use point-slope form**: 
   The equation of a line in point-slope form is:
   \[
   y - y_1 = m(x - x_1)
   \]
   Here, \( m = \frac{3}{2} \), and the point \( (x_1, y_1) = (-4, 10) \).

   Substituting the values:
   \[
   y - 10 = \frac{3}{2}(x + 4)
   \]

3. **Simplify the equation**: 
   Distribute the slope on the right-hand side:
   \[
   y - 10 = \frac{3}{2}x + \frac{3}{2} \times 4
   \]
   \[
   y - 10 = \frac{3}{2}x + 6
   \]
   Now, add 10 to both sides to solve for \( y \):
   \[
   y = \frac{3}{2}x + 6 + 10
   \]
   \[
   y = \frac{3}{2}x + 16
   \]

### Final Equation:
The equation of the line that is parallel to \( y = \frac{3}{2}x + 4 \) and passes through the point \( (-4, 10) \) is:
\[
y = \frac{3}{2}x + 16
\]

Would you like further details or have any other questions?

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Here are five related questions you might find interesting:
1. What is the slope of a line perpendicular to \( y = \frac{3}{2}x + 4 \)?
2. How do you find the equation of a line that passes through two given points?
3. Can a line be parallel to the x-axis or y-axis? If so, what would its equation be?
4. What changes in the equation of a line if it passes through the origin?
5. How do you determine the distance between two parallel lines?

**Tip**: For parallel lines, always remember that they have identical slopes!

Create an equation for a line that is parallel to the line y = 3/2x + 4 and passes through the point (-4, 10).

This problem demonstrates how to find the equation of a line that is parallel to y = 3/2x + 4 and passes through the point (-4, 10). Learn key algebraic concepts including slope-intercept and point-slope forms. Suitable for Grades 8-10.

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