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To find the equation of a line that passes through the two points \((-1, -6)\) and \((3, 4)\), we can follow these steps:

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

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

Substituting the given points \((-1, -6)\) and \((3, 4)\):

\[
m = \frac{4 - (-6)}{3 - (-1)} = \frac{4 + 6}{3 + 1} = \frac{10}{4} = 2.5
\]

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

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

Substitute \(m = 2.5\) and one of the points, say \((-1, -6)\):

\[
y - (-6) = 2.5(x - (-1))
\]

Simplifying:

\[
y + 6 = 2.5(x + 1)
\]

### Step 3: Simplify to slope-intercept form
Now, expand and simplify the equation:

\[
y + 6 = 2.5x + 2.5
\]

\[
y = 2.5x + 2.5 - 6
\]

\[
y = 2.5x - 3.5
\]

So, the equation of the line in slope-intercept form is:

\[
y = 2.5x - 3.5
\]

Would you like more details or have any questions about this solution?

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Here are 5 related questions you might find useful:
1. How do you find the equation of a line given the slope and a point?
2. Can you convert the equation into standard form?
3. What is the significance of the slope in the context of a real-world scenario?
4. How do you find the y-intercept of a line given two points?
5. What happens if the two points are vertical? How would the equation of the line change?

**Tip:** Always start by calculating the slope when given two points on a line, as it helps to form the equation step by step!

Find an equation for the line that passes through the points (-1, -6) and (3, 4).

Learn how to find the equation of a line passing through the points (-1, -6) and (3, 4). This problem covers key algebraic concepts, such as finding the slope and using the point-slope and slope-intercept forms to derive the final equation. Suitable for students in Grades 8-10.

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