Write the equation of the line that passes through the points (-8, -1) and (8,7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

To find the equation of the line that passes through the points \((-8, -1)\) and \((8, 7)\), we need to follow these steps:

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

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

Substitute the given points \((-8, -1)\) and \((8, 7)\):

\[
m = \frac{7 - (-1)}{8 - (-8)} = \frac{7 + 1}{8 + 8} = \frac{8}{16} = \frac{1}{2}
\]

So, the slope of the line is \(m = \frac{1}{2}\).

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

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

We can use either of the two points. Let’s use \((-8, -1)\):

\[
y - (-1) = \frac{1}{2}(x - (-8))
\]

### Step 3: Simplify the equation.
Simplifying the equation:

\[
y + 1 = \frac{1}{2}(x + 8)
\]

This is the equation in point-slope form. To simplify further if desired:

\[
y + 1 = \frac{1}{2}x + 4
\]

Subtract 1 from both sides:

\[
y = \frac{1}{2}x + 3
\]

### Final Answer:
The equation of the line in simplified form is:

\[
y = \frac{1}{2}x + 3
\]

Would you like more details or have any questions? 

Here are some related questions to consider:
1. What is the point-slope form and how does it differ from slope-intercept form?
2. How do you determine if a line is vertical or horizontal?
3. How can you verify that a point lies on a given line?
4. How would the equation change if the slope were negative?
5. What are the steps to graph a line using its equation?

**Tip:** Always remember that the slope represents the steepness of a line, and the sign of the slope indicates the direction.

Write the equation of the line that passes through the points (-8, -1) and (8, 7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Discover how to find the equation of a line that passes through the points (-8, -1) and (8, 7). This problem involves calculating the slope and using the point-slope form to find the final equation. Perfect for students in Grades 8-10 learning about linear equations and slope.

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