Find the equation of the lines that pass through each of the following points (1,3),(-3,-1)

To find the equation of a line passing through two given points \((1, 3)\) and \((-3, -1)\), we can follow these steps:

### Step 1: Find the slope (m)
The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

Substitute \((x_1, y_1) = (1, 3)\) and \((x_2, y_2) = (-3, -1)\) into the formula:

\[
m = \frac{-1 - 3}{-3 - 1} = \frac{-4}{-4} = 1
\]

### Step 2: Use point-slope form to find the equation
The point-slope form of the equation of a line is:

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

We can use either of the given points. Let's use \((1, 3)\):

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

Simplify the equation:

\[
y - 3 = x - 1
\]

\[
y = x + 2
\]

### Final equation:
The equation of the line passing through the points \((1, 3)\) and \((-3, -1)\) is:

\[
y = x + 2
\]

Would you like further clarification or a different approach? Here are 5 related questions to extend your understanding:

1. How do we find the equation of a vertical or horizontal line?
2. Can the slope of a line ever be undefined? If so, what does it mean?
3. What is the difference between point-slope form and slope-intercept form?
4. How would the equation change if the points were reversed?
5. How do you find the midpoint of two points?

**Tip:** The slope of a line indicates how steep the line is. A positive slope means the line rises, while a negative slope means it falls.

Learn how to find the equation of a line passing through the points (1, 3) and (-3, -1). This solution involves calculating the slope and using the point-slope form to derive the final equation in slope-intercept form. Suitable for students in Grades 8-10.

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