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?

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!