Write the equation of the line that passes through the points left parenthesis, 2, comma, 1, right parenthesis(2,1) and left parenthesis, minus, 4, comma, minus, 8, right parenthesis(−4,−8). 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 \((2, 1)\) and \((-4, -8)\), we need to 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 \((x_1, y_1) = (2, 1)\) and \((x_2, y_2) = (-4, -8)\):

\[
m = \frac{-8 - 1}{-4 - 2} = \frac{-9}{-6} = \frac{3}{2}
\]

### 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 \(m = \frac{3}{2}\) and the point \((2, 1)\):

\[
y - 1 = \frac{3}{2}(x - 2)
\]

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 convert the point-slope form to slope-intercept form?
2. What is the significance of the slope in a linear equation?
3. How do you find the x-intercept and y-intercept from the equation of a line?
4. What is the equation of a line parallel to this one passing through a different point?
5. How can you determine if two lines are perpendicular using their slopes?

**Tip:** Remember, the slope \(m\) tells you how steep the line is and the direction it goes.

Learn how to write the equation of a line passing through the points (2, 1) and (-4, -8) using the point-slope form of a line. This problem covers key concepts in geometry and coordinate geometry, including the slope formula and point-slope form. Suitable for students in Grades 7-9.

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