To find the equation of the line passing through the points \( (3, -1) \) and \( (7, -5) \), we will use the point-slope form of a line equation, which is given by:

\[
y - y_1 = m(x - x_1)
\]

### Step 1: Find the slope (\( m \))
The slope \( m \) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute \( (x_1, y_1) = (3, -1) \) and \( (x_2, y_2) = (7, -5) \):

\[
m = \frac{-5 - (-1)}{7 - 3} = \frac{-5 + 1}{4} = \frac{-4}{4} = -1
\]

### Step 2: Write the equation in point-slope form
Now that we know the slope is \( m = -1 \), we can use either point, \( (3, -1) \) or \( (7, -5) \), to write the equation. Let's use \( (3, -1) \):

\[
y - (-1) = -1(x - 3)
\]

Simplify:

\[
y + 1 = -1(x - 3)
\]

### Step 3: Simplify to slope-intercept form
Now, distribute and solve for \( y \):

\[
y + 1 = -x + 3
\]

Subtract 1 from both sides:

\[
y = -x + 2
\]

### Final Answer: 
The equation of the line is:

\[
y = -x + 2
\]

Would you like further details on any part of the process?

Here are five related questions for further practice:
1. Find the equation of the line passing through \( (2, 3) \) and \( (6, -1) \).
2. Convert \( y = 3x - 4 \) to standard form.
3. Find the slope of the line passing through \( (5, -2) \) and \( (-3, 4) \).
4. Determine if the points \( (1, 2) \), \( (2, 3) \), and \( (3, 4) \) are collinear.
5. Write the equation of a line parallel to \( y = 2x + 3 \) passing through \( (4, 5) \).

**Tip:** Remember, parallel lines always have the same slope!

The query submitted by the user: (3,-1) and (7,-5) write the equation

Learn how to find the equation of a line passing through the points (3, -1) and (7, -5) using the point-slope formula and slope-intercept form. This detailed solution is ideal for students in Grades 8-10 learning algebra and coordinate geometry.

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