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To find the equation of the line passing through the points \( (2, -6) \) and \( (-6, -4) \), we can use the **point-slope formula** for a line. The steps are as follows:

### Step 1: Find the Slope (m)
The formula for slope 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 \( (2, -6) \) and \( (-6, -4) \):
\[
m = \frac{-4 - (-6)}{-6 - 2} = \frac{-4 + 6}{-8} = \frac{2}{-8} = -\frac{1}{4}
\]

So, the slope \( m = -\frac{1}{4} \).

### Step 2: Use the Point-Slope Form
The point-slope form of a line equation is:
\[
y - y_1 = m(x - x_1)
\]

Using the point \( (2, -6) \) and the slope \( m = -\frac{1}{4} \):
\[
y - (-6) = -\frac{1}{4}(x - 2)
\]
Simplify:
\[
y + 6 = -\frac{1}{4}x + \frac{1}{2}
\]

### Step 3: Convert to Slope-Intercept Form
To get the equation in slope-intercept form \( y = mx + b \):
\[
y = -\frac{1}{4}x + \frac{1}{2} - 6
\]
\[
y = -\frac{1}{4}x - \frac{11}{2}
\]

### Final Answer
The equation of the line is:
\[
y = -\frac{1}{4}x - \frac{11}{2}
\]

Would you like further details or have questions?

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**Related Questions:**

1. How do you find the midpoint between two points?
2. What is the equation of a line perpendicular to this line?
3. How do you convert from point-slope form to standard form?
4. What if the points had the same x-coordinates or y-coordinates?
5. How do you calculate the distance between two points?

**Tip:** Always verify your slope calculation first, as it determines the accuracy of the final equation.

Find an equation for the line that passes through the points (2, -6) and (-6, -4).

Learn how to find the equation of a line passing through the points (2, -6) and (-6, -4). This solution covers essential algebraic concepts, including slope calculation and point-slope formula, suitable for Grade 9 students.

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