Write the equation of the line that passes through the points (−6,8) and (−8,2). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

To find the equation of the line passing through the points \((-6, 8)\) and \((-8, 2)\), we follow these steps:

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

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

Substituting the given points \((-6, 8)\) and \((-8, 2)\):

\[
m = \frac{2 - 8}{-8 - (-6)} = \frac{-6}{-2} = 3
\]

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

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

We can use either of the given points. Let's use the point \((-6, 8)\) and the slope \( m = 3 \).

Substituting into the point-slope form:

\[
y - 8 = 3(x - (-6)) 
\]

This simplifies to:

\[
y - 8 = 3(x + 6)
\]

### Step 3: Final simplified form
You can leave it in this form, which is the fully simplified point-slope form:

\[
y - 8 = 3(x + 6)
\]

This is the equation of the line passing through the points \((-6, 8)\) and \((-8, 2)\).

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Would you like more details or have any questions?

Here are 5 related questions:
1. How do you convert this point-slope form to slope-intercept form?
2. What if the line passes through \((-6, 8)\) and a vertical line at \(x = -6\)?
3. How do you find the perpendicular slope to this line?
4. Can you find the midpoint of the two points \((-6, 8)\) and \((-8, 2)\)?
5. How do you calculate the distance between these two points?

**Tip**: Remember that the point-slope form is especially useful when you already have the slope and a point on the line!

Discover how to write the equation of the line passing through the points (-6, 8) and (-8, 2) in fully simplified point-slope form. This problem explores key algebraic concepts like the slope formula and point-slope equation. Ideal for students in Grades 8-10.

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