To determine the equation of the line passing through the points \((-5, 3)\) and \( (1, 5) \), we can follow these steps:

1. **Find the slope \(m\)**:
   
   The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]

   Substituting the given points \((-5, 3)\) and \((1, 5)\):
   \[
   m = \frac{5 - 3}{1 - (-5)} = \frac{2}{6} = \frac{1}{3}
   \]

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

   Using the slope \(m = \frac{1}{3}\) and one of the points, say \((1, 5)\):
   \[
   y - 5 = \frac{1}{3}(x - 1)
   \]

3. **Simplify to the slope-intercept form \(y = mx + b\)**:
   
   \[
   y - 5 = \frac{1}{3}x - \frac{1}{3}
   \]
   \[
   y = \frac{1}{3}x - \frac{1}{3} + 5
   \]
   \[
   y = \frac{1}{3}x + \frac{14}{3}
   \]

Therefore, the equation of the line passing through the points \((-5, 3)\) and \((1, 5)\) is:
\[
y = \frac{1}{3}x + \frac{14}{3}
\]

Would you like more details on this solution, or do you have any other questions?

Here are 5 more questions you might find interesting:
1. How do you find the midpoint of a line segment?
2. How do you calculate the distance between two points in a plane?
3. What is the general form of the equation of a line?
4. How do you determine if two lines are parallel?
5. How can you find the perpendicular bisector of a line segment?

**Tip:** When working with linear equations, always double-check your slope calculations to ensure accuracy in your final equation.

Learn how to find the equation of a line passing through the points (-5, 3) and (1, 5) with step-by-step instructions. This problem covers key concepts in geometry and linear equations, including the slope formula, point-slope form, and slope-intercept form. Suitable for students in Grades 7-9.

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