Write the equation of the line that passes through the points left parenthesis, 3, comma, 9, right parenthesis(3,9) and left parenthesis, minus, 8, comma, 3, right parenthesis(−8,3). Put your answer in fully simplified *point-slope* form, unless it is a vertical or horizontal line.

To write the equation of the line that passes through the points \((3, 9)\) and \((-8, 3)\), we'll follow these steps:

### 1. Find the slope \(m\):
The slope \(m\) of the line passing 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 \((x_1, y_1) = (3, 9)\) and \((x_2, y_2) = (-8, 3)\):

\[
m = \frac{3 - 9}{-8 - 3} = \frac{-6}{-11} = \frac{6}{11}
\]

### 2. Write the equation in point-slope form:
The point-slope form of the equation of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using the slope \(m = \frac{6}{11}\) and the point \((3, 9)\):

\[
y - 9 = \frac{6}{11}(x - 3)
\]

This is the equation of the line in fully simplified point-slope form.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How do you find the slope-intercept form of this line?
2. What happens to the equation if the points were reversed?
3. How can you determine the midpoint between these two points?
4. What is the equation of the line perpendicular to this one passing through \((3, 9)\)?
5. How do you graph a line using the point-slope form?

**Tip:** The point-slope form is especially useful when you have the slope and a specific point on the line, making it easy to write the equation.

Learn how to write the equation of a line passing through the points (3, 9) and (-8, 3) using the point-slope form of a line equation. This problem involves finding the slope, determining the point-slope form, and understanding key concepts in coordinate geometry. Suitable for students in Grades 7-9.

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